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प्रश्न
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
उत्तर
`sec^4A - sec^2A = 1/cos^4A - 1/cos^2A`
= `(1 - cos^2A)/cos^4A`
= `sin^2A/cos^4A` [∵ `sin^2A = 1 - cos^2A`]
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Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
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