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Question
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
Solution
L.H.S = cot θ + tan θ
= `costheta/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/(sintheta*costheta)`
= `1/(sintheta*costheta)` ......[cos2θ + sin2θ = 1]
= `1/sintheta xx 1/costheta`
= cosecθ × secθ
= R.H.S.
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