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For acute angle theta, prove the followi...

For acute angle `theta`, prove the following:
`sec^2theta+cosec^2thetage4`

Text Solution

Verified by Experts

Using `A.M.geG.M.`
`(sin^2theta+cos^2thet)/2ge(sin^2thetacos^2theta)^(1//2)`
`rArr 1/2ge(sin^2thetacos^2theta)^(1//2)rArrsin^2thetacos^2thetale1/4`
`=sec^2thetacosec^2thetage4rArr(sin^2theta+cos^2theta)/(sin^2thetacos^2theta)ge4`
`rArr sec^2theta+cosec^2thetage4`
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CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
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  2. The circular wire of diameter 10 cm is cut and placed along the circum...

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  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

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  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

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  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

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  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

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  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

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  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

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  17. Which of the following is true ?

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  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  19. Which of the following is greatest ?

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  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

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  21. Which of the following is not correct ?

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