Question

Sin x cot x+sin x cosec x=1+cos x

Answer 1

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$\large\sf\implies\: Sinx\: cotx + sinx\: cosecx=1 +\: cos x$

$\large\sf\implies\: sinx\dfrac{cosx}{sinx}+sinx\dfrac{1}{sinx}$

$\large\sf\implies\cancel{sinx}\dfrac{cosx}{\cancel{sinx}}+\cancel{sinx}\dfrac{1}{\cancel{sinx}}$

$\huge\sf\implies\:1+cosx$

$\large\sf\implies\:LHS=RHS$

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Answer 2

Solution :

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We know that,

1 ) cotx = cosx/sinx

2 ) cosecx = 1/sinx

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LHS = sinxcotx + sinxcosecx

= sinx( cosx/sinx ) + sinx( 1/sinx )

After cancellation, we get

= cosx + 1

= RHS

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