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If theta lies in the first quardrant and...

If `theta` lies in the first quardrant and `costheta=(8)/( 17 )`, then find the value of `cos(30^(@)+theta)+cos(45^(@)-theta)+cos(120^(@)-theta)`.

A

`23/17((sqrt3-1)/(2)+(1)/(sqrt2))`

B

`23/17((sqrt3+1)/(2)+(1)/(sqrt2))`

C

`23/17((sqrt3-1)/(2)-(1)/(sqrt2))`

D

`23/17((sqrt3+1)/(2)-(1)/(sqrt2))`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
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  2. In a right angled triangle, the hypotenuse is four times as long as th...

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  3. If theta lies in the first quardrant and costheta=(8)/( 17 ), then fi...

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  4. cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8)=

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  6. In a triangle ABC, sin A-cosB=cosC, then angle B, is

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  7. If theta lies in the first quadrant which of the following in not true

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  8. cos2 theta+2 costheta is always

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  9. The interior angles of a polygon are in AP The smallest angle is 120 a...

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  10. The maximum and minimum values of -4le5cos theta+3cos(theta+(pi)/(3...

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  12. If A=tan6^0tan42^0 and B=cot66^0cot78^0 , then

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  13. If sinx+cosesx=2,thensin^(n)x+cosec^(n)x is equal to

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  14. If x/acosalpha+y/bsinalpha=1, x/acosbeta+y/bsinbeta=1 and (cos alpha c...

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  15. The value of theta lying between 0 and pi/2 and satisfying |[1+sin^2th...

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  16. The value of sqrt3cot20^(@)-4cos20^(@) is

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  17. sqrt(3)cossec2 0^0-sec2 0^0

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  18. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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  19. The value of sin(pi+theta)sin(pi-theta)cosec^(2)theta is equal to

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  20. If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , then show that (tanx)/(tany)=(...

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