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Question
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
Options
True
False
Solution
This statement is True.
Explanation:
`sqrt((1 - cos^2 theta) sec^2 theta)`
= `sqrt(sin^2 theta * sec^2 theta)` ...[∵ sin2θ + cos2θ = 1]
= `sqrt(sin^2 theta * 1/(cos^2 theta)` ...`[∵ sec theta = 1/costheta, tan theta = sin theta/cos theta]`
= `sqrt(tan^2 theta)`
= tan θ
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