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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=`

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 PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
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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=

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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 secalpha and cosecalpha are the roots of the equation x^2-px+q=0, t...

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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=1n then the value of cos^12x+3cos^10x+3cos^8x+cos^6x-1 ...

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

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

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  10. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

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  11. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

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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. sec^2theta=4xy/(x+y)^2 is true if and only if

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  19. If sinx+siny+sinz=3," then "cosx+cosy+cosz is equal to

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  20. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+si...

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