## HOW TO PROVE TRIGONOMETRIC IDENTITIES || TRIGONOMETRY

## Electronic Payment and Application system of System of scholarship

## If you want to apply for scholarship and if you are from HP then click on the above link to proceed further.

H.P. bonafide students, studying within state or outside state, within India, having valid AADHAAR (UID / EID) Credentials and fulfilling the Scheme specific guidelines are eligible to apply under these scholarship schemes.

H.P. bonafide students, studying in Class IX onwards, within state or outside state, within India, can apply online under these schemes

Students can apply as per the time schedule notified vide newspapers and HP ePASS website, from time to time.

you cannot apply as a fresh if you are a Renewal candidate. Your application will be rejected in that case.

You can fill up the online application in as many sittings as you wish, until you are satisfied that you have entered all desirable fields correctly. The software provides facility to save your application at every stage until you click on 'submit & finalize' button.

You can edit information filled by you until you finalize and submit the online application.

Go to the option "Student login" then enter your Username and Passwordto edit the application.

You should take a print out of the application then sign and send it immediately with requisite documents to the State Department after authenticating the application from your institute.

Fields provided with red asterisk(*) mark are mandatory fields.

You can edit all fields except a few like parental income, mobile no. email Id etc. It may be noted that once you click on "Finalize and submit" button your application will be forwarded to the next level and then you cannot edit further.

You should separately inform the mistakes detected by you to the Institute/District/Region/State. The software provides facility at the level of the Institute & State to edit& correct limited information.

Except some basic parameters like religion, name of institution, parental annual income & bank details, the Institute/State can edit other fields. However, corrections made by the Institute/State, if any, would be conveyed instantly to the student through SMS/email. What the student had filled up and the correction made by the Institute/State both would show up.

UID number otherwise known as 'AADHAAR' number is Unique Identification Number given by Unique Identification Authority of India (UIDAI). The AADHAAR Number should be mapped with the Bank Account in which Scholarship Amount is desired to be transferred. For this the concerned Bank may be contacted with a copy of the AADHAAR card.

How to prove Identity cos 6x = 32cos

H.P. bonafide students, studying in Class IX onwards, within state or outside state, within India, can apply online under these schemes

Students can apply as per the time schedule notified vide newspapers and HP ePASS website, from time to time.

you cannot apply as a fresh if you are a Renewal candidate. Your application will be rejected in that case.

You can fill up the online application in as many sittings as you wish, until you are satisfied that you have entered all desirable fields correctly. The software provides facility to save your application at every stage until you click on 'submit & finalize' button.

You can edit information filled by you until you finalize and submit the online application.

Go to the option "Student login" then enter your Username and Passwordto edit the application.

You should take a print out of the application then sign and send it immediately with requisite documents to the State Department after authenticating the application from your institute.

Fields provided with red asterisk(*) mark are mandatory fields.

You can edit all fields except a few like parental income, mobile no. email Id etc. It may be noted that once you click on "Finalize and submit" button your application will be forwarded to the next level and then you cannot edit further.

You should separately inform the mistakes detected by you to the Institute/District/Region/State. The software provides facility at the level of the Institute & State to edit& correct limited information.

Except some basic parameters like religion, name of institution, parental annual income & bank details, the Institute/State can edit other fields. However, corrections made by the Institute/State, if any, would be conveyed instantly to the student through SMS/email. What the student had filled up and the correction made by the Institute/State both would show up.

UID number otherwise known as 'AADHAAR' number is Unique Identification Number given by Unique Identification Authority of India (UIDAI). The AADHAAR Number should be mapped with the Bank Account in which Scholarship Amount is desired to be transferred. For this the concerned Bank may be contacted with a copy of the AADHAAR card.

How to prove Identity cos 6x = 32cos

^{6}x - 48cos^{4}x + 18cos^{2}x - 6cos^{2}x - 1### Proof

L.H.S. = cos 6x = cos (3.2x)

Now using the result cos 3Î¸ = 4cos3 Î¸ - 3 cos Î¸

= 4cos3 2x - 3 cos 2x

Now using the result 1 + cos 2Î¸ = 2 cos2 Î¸

⇒ cos 2Î¸ = 2 cos2 Î¸ -1

= 4 {2 cos2 x -1 }3 - 3 {2 cos

^{2}x -1}

Now using the result {a - b }

^{3}= {a}^{3}- { b }^{3}- 3{a }^{2}b +3(a) b^{2}cos 6x =4[ {2cos

^{2}x }

^{3}-{ 1 }

^{3}- 3{2cos

^{2}x }

^{2}1 +3(2cos

^{2}x) 1

^{2}] - 3

**×**{2 cos

^{2}x -1}

cos 6x = 4[ 8cos

^{6}x - 1 - 12cos^{4}x + 6cos^{2}x] - 3{2cos^{2}x-1}
cos 6x = 32cos

^{6}x - 4 - 48cos^{4}x + 24cos^{2}x - 6cos^{2}x + 3
cos 6x = 32cos

^{6}x - 48cos^{4}x + 18cos^{2}x - 6cos^{2}x - 1##
Prove the Identity

##
tan (2x) = 2tan x 1 - tan^{2} x

**Proof**

We know that

tan (A+B) = tan A + tan B1 - tan A tan B

Put A = B = x in above formula . then it becomes

tan (x+x) = tan x + tan x1 - tan x tan x

tan (2x) = 2tan x 1 - tan

tan (x+x) = tan x + tan x1 - tan x tan x

tan (2x) = 2tan x 1 - tan

^{2}x## Prove that sin 2x = 2sin x cos x

**Proof**

As we know that sin (A + B) = sin A cos B + cos A sin B.. ...(1)

Put A = B = x in ... (1)

sin (x + x) = sin x cos x + cos x sin x

sin (2x) = sin x cos x + sin x cos x

sin (2x) = 2 sin x cos x

##
Prove that cos 2x = cos^{2} x - cos^{2} x

**Proof**

As we know that cos (A + B) = cos A cos B - sin A sin B.. ...(1)

cos (x + x) = cos x cos x - sin x sin x

cos 2x = cos

^{2}x - sin

^{2}x

^{ }