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Question
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Options
−1
1
0
None of these
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Solution
Given:
`sin θ+sin^2θ=1`
`⇒ 1-sin^2θ= sin θ`
Now,
`cos^2θ+cos^4θ`
`= cos^2 θ+cos^2θcos^2θ`
=` cos^2θ+(1-sin^2θ)(1-sin^2θ)`
`=cos^2θ+sinθ sinθ`
`=cos^2 θ+sin^2θ`
`=1`
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Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
