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

If `sin x + sin y = a` and `cos x + cos y = b`, what is sin `x.sin y + cos x .cos y `equal to ?

A

`a+ b ab`

B

`a +b+ab`

C

`a^(2) + b^(2) -2`

D

`(a^(2) + b^(2) -2)/2`

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The correct Answer is:
D
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LUCENT PUBLICATION-ELEMENTARY TRIGONOMETRIC IDENTITIES -EXERCISE 11A
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  2. If cosx/(1 + cosec x)+ (cosx)/(cosecx -1) =2, which one of the followi...

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  3. If sin x + sin y = a and cos x + cos y = b, what is sin x.sin y + cos ...

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  4. If a is an angle in first quadrant such that "cosec"^(4) alpha = 17+"c...

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  5. If x + (1//x) = 2 cos alpha, then what is the value of x^2 + (1//x^2) ...

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  6. If sin theta + cos theta = a and sec theta + "cosec" theta = b, then w...

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  7. Among given values of theta which one satisfies the equation (cos thet...

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  8. If 7 cos^2 theta +3 sin^2 theta =4 and 0 lt theta lt pi//2, what is th...

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  9. What is the value of , [(1-sin^(2)theta)sec^(2)theta +tan^(2)theta](co...

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  10. What is the value of sin^(2) 15^(@) + sin^(2) 20^(@) + sin^(2)25^(@) +...

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  11. What is sqrt((1 + sin theta)/(1 -sintheta)) equal to ?

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  12. If theta^(@) lt theta lt 90^(@) and (sin theta)/(cos theta) + (cos the...

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  13. If sin 3 theta = cos (theta - 2 ^(@)) where 3 theta and (theta - 2 ^(@...

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  14. What is ( sin ^(6) theta - cos ^(6) theta )/( sin ^(2) theta - cos ^(2...

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  15. If sin^(4)x + sin^(2) x =1, then the value of cot^(4)x + cot^(2)x is:

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  16. If x cos theta + y sin theta =2 and x cos theta - y sin theta =0, then...

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  17. Expression sin A (1 + tan A) + cos A(1+ cot A) is equal to:

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  18. If 0^(@) lt theta lt 90^(@) and cos^(2) theta - sin^(2) theta = 1/2,th...

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  19. If 3 sin theta + 4 cos theta = 5, then 3 cos theta - 4 sin theta is eq...

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  20. (1-sinAcosA)/(cosA(secA-cosecA)).(sin^(2)A-cos^(2)A)/(sin^(3)A+cos^(3)...

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