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If x-1/x = 2i sin theta, "show that", x^...

`If x-1/x = 2i sin theta, "show that", x^(4)-1/x^(4)=2i sin 4 theta.`

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If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos theta +y^(2)=sin ^(2) theta

If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = sin theta (1 + cos2 theta) + sin 2 theta(1 + cos theta), "show that" u^(2) + v^(2) = 4(1 + cos theta) (1 + cos 2theta).

If x= cos theta+ I sin theta and y= cos psi + I sin psi , then show that (x)/(y)+(y)/(x)= 2 cos (theta- psi) .

If cos^(-1)x+cos^(-1)y= theta , show that x^2-2xycos theta+y^2 = sin^2 theta .

If sin^4theta+sin^2 theta=1 show that, tan^4theta-tan^2theta=1 .

If sin ( pi cos theta ) = cos (pi sin theta ), , then show that theta =+- (1)/(2) sin ^(-1)""(3)/(4)

If x+iy=(3)/(2+cos theta + sin theta),"prove that" , x^(2)+y^(2)=4x-3.

If x sin theta = y sin ( theta + (2pi)/3) = z sin ( theta+ (4pi)/3), then the value of xy+yz+zx will be-

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS OF MULTIPLE ANGLES-Long Answer Type Questions
  1. If" " n tan alpha = (n+1) tan beta " then show that", tan (alpha - bet...

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  2. If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (ta...

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  3. If tan theta = sec 2 alpha, "show that", sin 2 theta = (1-tan^(4) alph...

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  4. Prove that,8 cos^(4) theta = 3 + 4 cos 2 theta + cos 4 theta

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  5. Prove that,8 sin^(4) theta = 3 - 4 cos 2 theta + cos 4 theta

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  6. Prove that,64cos^(3) theta sin^(4) theta = cos 7 theta - cos 5 theta -...

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  7. Prove that,sin^(2)A cos^(4) A = 1/16 + 1/32 cos2A - 1/16 cos 4 A - 1/3...

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  8. If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show th...

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  9. If " "alpha " and " beta " are positive acute angles and " cos 2 alpha...

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  10. "If " (tan x)/(tan y) = (1 + cos^(2) x)/(1 + sin^(2) x ) " show that "...

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  11. If sin theta + sin 2 theta = a " and " cos theta + cos 2 theta = b, "...

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  12. If theta = pi/(2^(n) + 1), "show that",2^(n) cos theta cos 2 theta cos...

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  13. Prove that, (2 cos theta - 1)(2 cos 2 theta-1)(2 cos2^(2) theta-1)...(...

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  14. If x-1/x = 2i sin theta, "show that", x^(4)-1/x^(4)=2i sin 4 theta.

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  15. Show that,(x tan alpha + y cot alpha)( x cot alpha + y tan alpha) = (x...

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  16. If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = s...

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  17. Eliminate theta : x = a ( cos theta + cos 2 theta), y = b ( sin theta ...

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  18. "If " a sin theta + b cos theta = c " and " a cosec theta + b sec thet...

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  19. "If "0ltalphaltpi/2 " and " sin alpha + cos alpha + tan alpha + cot a...

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  20. If sin (x + y) = p/sqrt(1 + p^(2)) " and " cos (x - y) = 1/sqrt(1 + q^...

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