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If x=a cos theta + b sin theta and y=a ...

If `x=a cos theta + b sin theta and y=a sin theta - b cos theta.` then` a ^(2) +b^(2) ` is equal to

A

`a^(2) - b^(2) = p^(2) -q^(2)`

B

` a^(2) + b^(2) = p ^(2) + q^(2)`

C

`a+b=p+q`

D

`a-b=p-q`

Text Solution

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The correct Answer is:
B
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ML KHANNA-TRIGONOMETRY RATIOS AND IDENTITIES-PROBLEM SET (3) ( MULTIPLE CHOICE QUESTIONS)
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  3. If sin A + cos A = p, sin^(3) A + cos^(3) A=q, then

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  4. If x=sectheta-tantheta, and y=cosectheta+cottheta, then

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  5. If:x/a costheta+y/b s intheta=1a n dx/a s intheta-y/bcostheta=1, Prov...

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  6. If x=a cos theta + b sin theta and y=a sin theta - b cos theta. then ...

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  7. If p sec theta - b tan theta =a and q sec theta +a tan theta =b, then

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  8. If a+b tan theta = sec theta and b - a tan theta = 3 sec theta, then ...

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  9. For 0 lt phi le ( pi )/( 2), if x = sum(n=0)^(oo) cos^(2n) phi , y = s...

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  10. If tan x = ( 2b )/( a-c) , ( a cancel(=)c) y = a cos ^(2) x + 2b sin...

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  11. If sin x + cos x = sqrt( 2) cos x , then cos x - sin x is equal to

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  12. If theta is an acute angle and sin"" ( theta )/( 2) = sqrt((x-1)/( 2x)...

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  13. If a cos theta - b sin theta =c, " then" a sin theta + b cos theta is...

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  14. If sin A + sin 2A =x and cos A + cos 2A = y, then ( x^(2) + y^(2) ) ( ...

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  15. It is given that cos(theta-alpha)=a, cos(theta-beta)=b What is...

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  16. If a sin^(2)x+b cos^(2)x=c, b sin^(2)y+a cos^(2)y=d and atan x=btany t...

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  18. If (x)/(cos theta)=(y)/(cos(theta-(2pi)/(2)))=(2)/(cos(theta+(2pi)/(3)...

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  19. If x sin theta = y sin ( theta + ( 2pi )/( 3)) = z sin( ( theta + 4pi ...

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  20. |{:(cos ( theta +A), sin ( theta +A),1),(cos ( theta +B),sin ( theta +...

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