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प्रश्न
If cos A + cos2A = 1, then sin2A + sin4 A = ?
उत्तर
cos A + cos2A = 1 ......[Given]
∴ cos A = 1 – cos2A
∴ cos A = sin2A ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`
∴ cos2A = sin4A .....[Squaring both the sides]
∴ 1 – sin2A = sin4A
∴ 1 = sin4A + sin2A
∴ sin2A + sin4A = 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)`
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= R.H.S
