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If cos alpha + cos beta + cos gamma =3 ...

If ` cos alpha + cos beta + cos gamma =3 , " then " sin alpha + sin beta + sin gamma = `

A

3

B

2

C

1

D

0

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If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that sin 3 alpha + sin 3 beta + sin 3 gamma = 3 sin ( alpha + beta + gamma)

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos ( alpha + beta + gamma)

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that cos ( alpha + beta) + cos ( beta + gamma) + cos ( gamma + alpha) = 0

If cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin gamma , Prove that cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 3/2 = sin^(2) alpha + sin^(2) beta + sin^(2) gamma .

Assertion (A): If A, B, C are the angles of a triangle such that cos A + cos B + Cos C = 0 = sin A + sin B + sin C then cos 3A + cos 3B + cos 3C = -3 Reason (R) : If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + singamma then cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos (gamma+alpha+beta)

Let alpha, beta, gamma satisfy 0 lt alpha lt beta lt gamma lt 2pi and cos(x+alpha) + cos(x + beta) + cos(x + gamma) =0 for all x in R observe the following statements. Statements-I: gamma - alpha =(2pi)/3 Statement-2: cos alpha + cos beta + cos gamma=0 and sin alpha + sin beta + sin gamma=0

Let A and B denote the statements A: cos alpha + cos beta + cos gamma=0, B:sin alpha + sin beta + sin gamma=0 , If cos(beta - gamma) + cos(gamma - alpha) + cos(alpha - beta)=-3/2 , then

If x=r cos alpha cos beta cos gamma , y= cos alpha cos beta sin gamma , z= r sin alpha cos beta , mu = r sin beta " then " x^(2)+y^(2) + z^(2)+mu^(2)=

DIPTI PUBLICATION ( AP EAMET)-TRIGONOMETRIC RATIOS AND IDENTITIES -EXERCISE 1 A ( TRIGONOMETRIC FUNCTIONS)
  1. If sin x + sin^(2) x =1 " then " cos^(8) x + 2 cos^(6) x + cos^(4) x...

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  2. If cos x + cos^(2) x =1 , " then " sin^(12) x + 3 sin^(10)x + 3sin^(8...

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  3. If cos alpha + cos beta + cos gamma =3 , " then " sin alpha + sin bet...

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  4. If sin theta 1+ sin theta 2+ sin theta 3=3 " then " cos theta 1 + cos...

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  5. If sin theta , cos theta are ther roots of the equation ax^(2)-bx+c...

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  6. If k=(1+ sin A) (1+ sin B)(1+ sin C)=(1- sin A) (1- sin B) (1- sin C) ...

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  7. If k=( sec A + tan A) ( sec B+ tan B) sec C + tan C)=(sec A - tan A)(s...

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  8. If sec theta =a+(1)/(4a) " then " sec theta + tan theta =

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  9. If "cosec " theta =p+(1)/(4p) , " then cosec " theta + cot theta =

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  10. If "cosec"^(2) theta = (4xy)/((x+y)^(2)), then

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  11. If a sin x = b cos x =(2c tan x )/(1- tan^(2) x) " then " ((a^(2)-b^(...

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  12. If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1...

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  13. sqrt(1-sin^(2)100^(@))*sec 100^(@)=

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  14. sqrt((1+sinA)/(1-sin A ))=

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  15. If sqrt((1+ cos theta )/(1- cos theta ))="cosec " theta + cot theta " ...

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  16. If x=a cos^(3) theta , y= a sin^(3) theta then

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  17. If x= a cos^(4) theta, y=bsin^(4) theta , then sqrt(x//a) + sqrt(y//...

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  18. If x cos theta + y sin theta = a , x sin theta - y cos theta = b the...

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  19. If sin theta + cos theta = m and sec theta + " cosec " theta = n the...

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  20. If (x)/(a) cos theta + (y)/(b) sin theta = 1 , (x)/(a) sin theta - (y...

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