Math, asked by prishalahe, 3 months ago

prove this guys correct answer is needed


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Answered by venkataramaboddu7
1

here is ur answer

hope it's help you

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Answered by AAnand2000
1

Answer:

Let's solve the LHS,

I am solving by taking x instead of θ, as I am unable to form an equation on this platform using θ,

LHS = \frac{Cosecx + Cotx}{Cosecx - Cotx}

Converting the equation in sin and cos form,

= \frac{\frac{1}{Sinx} + \frac{Cosx}{Sinx}  }{\frac{1}{Sinx} - \frac{Cosx}{Sinx} }

= \frac{\frac{1 + Cosx}{Sinx} }{\frac{1 - cosx}{Sinx} }

Eliminating the sinx, we will get:

= \frac{1 + Cosx}{1 - Cosx}

Multiplying Numerator and denominator by (1 + Cosx)

=  \frac{1 + Cosx}{1 - Cosx} X \frac{1 + Cosx}{1 + cosx}

= \frac{(1 + Cosx)^{2} }{ 1 - Cos^{2}x }

Solving (1 + cosx)^{2} and Putting 1 - cos^{2} x = Sin^{2}x, we will get:

= \frac{1 + cos^{2}x + 2cosx }{sin^{2}x }

= \frac{1}{Sin^{2}x } + \frac{Cos^{2} x}{Sin^{2}x } + \frac{2Cosx}{Sin^{2}x }

Taking the equation in cosec and cot form,

= Cosec^{2} x + Cot^{2} x + 2 Cosecx Cotx

= (Cosecx + Cot x)² = RHS

∴ Proved

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