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Prove that: cos^2 45^@-sin^2 15^@=(sqrt(...

Prove that: `cos^2 45^@-sin^2 15^@=(sqrt(3))/4`

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To prove that \( \cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4} \), we can follow these steps: ### Step 1: Use the identity for cosine and sine We can use the identity: \[ \cos^2 A - \sin^2 B = \cos(A + B) \cdot \cos(A - B) \] Here, we will set \( A = 45^\circ \) and \( B = 15^\circ \). ...
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RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If tanA=5/6 and tanB=1/(11),\ p rov e\ t h a t\ A+B=pi/4

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  2. If tanA=m/(m-1)\ and tanB=1/(2m-1), then prove that A-B=\ pi/4

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  3. Prove that: cos^2 45^@-sin^2 15^@=(sqrt(3))/4

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  4. Prove that: sin^2(n+1)A-sin^2n A="sin"(2n+1)A s in A

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  5. Prove that: (sin(A+B)+sin(A-B))/(cos(A+B)+cos(A-B))=t a n A

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  6. Prove that: (sin(A-B))/(cos A cosB)+(sin(B-C))/(cos B cos C)+(sin(C-A)...

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  7. Prove that: ("sin"(A-B))/(s in A s in B)+("sin"(B-C))/(s in B s in C)+...

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  8. Prove that: sin^2B=sin^2A+sin^2(A-B)-2sin A cos B sin(A-B)

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  9. Prove that: cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)

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  10. Prove that: (tan(A+B))/(cot(A-B))=\ (tan^2A-tan^2B)/(1-tan^2Atan^2B)

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  11. If tan A= xtanB then prove that sin(A-B)/sin(A+B)=(x-1)/(x+1)

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  12. If tan(A+B)=x and tan(A-B)=y then find the values of tan2A and tan2B

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  13. If cos A+sin B=m and sin A+cos B=n , prove that 2sin(A+B)=m^2+n^2-2.

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  14. If tan A+tan B=a and cot A+cot B=b , prove that: cot(A+B)=1/a-1/b

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  15. If sin(alpha+beta)=1 and sin(alpha-beta)=1/2, where 0lt=alpha, betalt=...

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  16. If alpha, beta are two different values of x lying between 0 and 2pi ...

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  17. Prove that (tan^2 (2theta)-tan^2 theta)/(1-tan^2 (2theta) tan^2 theta)...

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  18. If s inalphas inbeta-cosalphacosbeta+1=0, then prove that 1+cotalphata...

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  19. If t a nalpha=x+1,tanbeta=x-1, show that 2cot(alpha-beta)=x^2dot

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  20. Find the maximum and minimum values of 7\ costheta+24 s intheta

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