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Q1. prove that(sin A + COSA) (tanA+cotA)=sinA-cosecA​

Answer»

Step-by-step EXPLANATION:

CORRECT QUESTION :-

PROVE :-

\sf ( sinA+cosA)(tanA+cotA) = secA+cosecA

Solution :-

L.H.S = (sinA+cosA)(tanA+cotA)

\bullet\bf \ tanA = \dfrac{sinA}{cosA}

\bullet\bf \ cotA= \dfrac{cosA}{sinA}∙

= \sf (sinA+cosA) \left( \dfrac{sinA}{cosA} +\dfrac{cosA}{sinA} \right)

= \sf (sinA+cosA) \left( \dfrac{sin^2A+cos^2A}{sinAcosA} \right)

\bullet \bf \ sin^2A+cos^2A = 1

= \sf (sinA+cosA) \times \left( \dfrac{1}{sinAcosA} \right)

= \sf \dfrac{sinA}{sinAcosA} \times \dfrac{cosA}{sinAcosA}

= \sf \dfrac{1}{cosA}+\dfrac{1}{sinA}

\bullet \bf \ secA= \dfrac{1}{cosA}∙

\bullet \bf \ cosecA= \dfrac{1}{sinA}∙

= \sf secA+cosecA

= R.H.S

Hence PROVED.


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