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Prove that sin^2(theta-phi)-sin^2(theta+...

Prove that `sin^2(theta-phi)-sin^2(theta+phi)= -sin2theta sin2phi` hence prove that `cos2thetacos2phi-sin^2(theta+phi)+sin^2(theta-phi)=cos(2theta+2phi)`

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A N EXCEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove that sin120^@ cos330^@ +cos240^@ sin330^@=1

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  2. Prove that cos420^@ sin390^@+cos(-300^@)sin(450^@)=3/4

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  3. Prove that sin^2(theta-phi)-sin^2(theta+phi)= -sin2theta sin2phi hence...

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  4. Given that tan(A+B)=(tanA+tanB)/(1-tanAtanB) by writing A+B+C=(A+B)+C...

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  5. Given that tan(A+B)=(tanA+tanB)/(1-tanAtanB) if A+B+C=0^@ prove that t...

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  6. Prove that sin(A+B)sin(A-B)=sin^2A-sin^2B

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  7. Given that sin18^@=(sqrt5-1)/4 prove thatsin^2 24^@-sin^2 6^@=(sqrt5-1...

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  8. Express sinA+sin3A and cosA+cos3A in product form

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  9. Prove that (sinx+sin3x)/(cosx+cos3x)=tan2x

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  10. If A=30^@ deduce the value of tan60^@

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  11. Express sintheta+sin3theta and sin5theta+sin7theta in product form

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  12. Prove that sintheta+sin3theta+sin5theta+sin7theta=4costhetacos2thetasi...

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  13. Express cos40^@ cos80^@ in sum form

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  14. Prove that cos20^@ cos40^@ cos80^@=1/8

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  15. Express sin3A and cos2A in terms of sine function

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  16. Convert sin5A+sinA into product form and show that sin5A=5sinA-20sin^3...

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  17. If A=18^@ deduce the value of sin36^@=sqrt(10-2sqrt5)/4

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  18. Prove that cos^2theta=(1+cos2theta)/2

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  19. Evaluate cos^2(pi/8)+cos^2((3pi)/8)

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  20. Evaluate cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)=2

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