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प्रश्न
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
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उत्तर
We know that `sin^2 theta + cos^2 theta = 1`
So
`tan^2 theta cos^2 theta = (tan theta xx cos theta)^2`
`= (sin theta/cos theta xx cos theta)^2`
`= sin^2 theta`
`= 1 - cos^2 theta`
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संबंधित प्रश्न
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tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
= `tan^2θ xx square` ...[1 – cos2θ = sin2θ]
= R.H.S.
