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If sinA+sin^2A=1, then the value of cos^...

If `sinA+sin^2A=1,` then the value of `cos^2A+cos^4A` is

A

1

B

`1/2`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Given, sin A + `sin^(2)A=`
`rArr sinA= 1-sin^(2)A=cos^(2)A` `[therefore sin^(2)theta+cos^(2)theta=1]`
On squaring both sides, we get
`rArr sin^(2)A=cos^(4)A`
`rArr 1-cos^(2)A=cos^(4)A`
`rArr cos^(2)A+ cos^(4)A=1`
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NCERT EXEMPLAR ENGLISH-INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS-LONG ANSWER TYPES QUESTIONS
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  3. Prove that sqrt(sec^(2)theta + cosec^(2)theta) = tantheta + cottheta.

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  5. If 1+sin^(2)theta = 3sinthetacostheta, then prove that tantheta=1 or 1...

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  6. If sintheta + 2 costheta=1,then prove that 2sintheta-costheta=2.

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  8. The shadow of a tower standing on a level ground is found to be 40 m ...

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  9. A vertical tower Stands on a horizontal plane and is surmounted by a v...

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  10. if tantheta+sectheta=l then prove that sectheta=(l^2+1)/(2l)

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  11. If sin theta+ cos theta = p and sec theta + cosec theta = q; show that...

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  12. If a sintheta + bcos theta = C, then prove that a costheta -b sintheta...

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  13. Prove that (1+sectheta-tantheta)/(1+sectheta+tantheta) = (1-sintheta)/...

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  14. The angle of elevation of the top of a tower 30 m high from the foot ...

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  15. From the top of a tower h m high, angles of depression of two objects,...

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  17. The angle of elevation of the top of a vertical tower from a point on ...

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  18. If the angle of elevation of a cloud from a point h metres above a lak...

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