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If sec^4theta+sec^2theta=10+tan^4theta+t...

If `sec^4theta+sec^2theta=10+tan^4theta+tan^2theta,` then `sin^2theta=` `2/3` (b) `3/4` (c) `4/5` (d) `5/6`

A

`2/3`

B

`3/4`

C

`4/5`

D

`5/6`

Text Solution

Verified by Experts

The correct Answer is:
C
`sec^4theta+sec^2theta=10+tan^4theta+tan^2theta`
`rArrsec^4theta-tan^4theta+sec^4theta-tan^2theta=10`
`rArr sec^2theta+tan^2theta+1=10`
`rArr2sec^2theta=10`
`rArrcos^2theta=1/5`
`rArr sin^2theta=4/5`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. If cosectheta-cottheta=q, then the value of cosectheta is

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  2. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

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  3. If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta, then sin^2theta= 2...

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  4. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

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  5. If sec alphaa n dalpha are the roots of x^2-p x+q+0, then p^2=q(q-2) ...

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  6. Which of the following is not the quadratic equation whose roots are c...

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  7. If sinx+sin^2x=1, then find the value of cos^(12)x +3cos^(10)x + 3 cos...

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  8. 3(sintheta-costheta)^4+6(sintheta +costheta)^2+4(sin^6theta+cos^6theta...

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  9. If sinx+sin^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

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  10. (1+tanalphatanbeta)^2+(tan"alpha"-tan"beta")^2= tan^2alphatan^2beta ...

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  11. about to only mathematics

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  12. A circle is drawn in a sector of a larger circle of radius r , as show...

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  13. A right triangle has perimeter of length 7 and hypotenuse of length 3....

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  14. Given that the side length of a rhombus is the geometric mean of the ...

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  15. Which of the following is correct?

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

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  17. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

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  18. The equation sec ^2 theta = ( 4xy )/( ( x+y)^2) is possible for x...

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  19. If sintheta1+sintheta2+sintheta3, then costheta1+costheta2+costheta3 i...

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  20. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

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