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प्रश्न
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
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उत्तर
LHS = `(cosecθ)/(tanθ + cotθ)`
= `(1/sinθ)/(sinθ/cosθ + cosθ/sinθ)`
= `(1/sinθ)/((sin^2θ + cos^2θ)/(cosθsinθ))` = `(1/sinθ)/(1/(cosθsinθ)`
= `1/sinθ xx (cosθsinθ)/1 = cosθ`
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Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
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Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
