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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 ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
  1. If costheta+sintheta=sqrt(2)costheta, show that costheta-sintheta=sqrt...

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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. Find the value of cos^(4)""(pi)/(8)+cos^(4)""(3pi)/(8)+cos^(4)""(5pi)/...

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  5. If tan(A+B)=pand tan(A-B)=q, then the value of tan2A, is

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  6. In a tringle 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 A.P. the smallest angle is 120...

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

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  11. Prove that: sin36^0s in 72^0s in 108^0s in 144^0=5/(16)dot

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

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  13. If sinx+cosecx=2," then "sin^nx+cosec^nx is equal to

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  14. If (x)/(a) cos alpha+ (y)/(b) sin alpha = 1, (x)/(a) cos beta + (y)/(b...

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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 vlaue of sqrt3cot20^(@)-4cos20^(@), is

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  17. Show that sqrt(3)\ cos e c\ 20^0-sec20^0=4.

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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) , show that (tanx)/(tany)=a/b .

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