Question

prove this guys correct answer is needed


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Answer 1

here is ur answer

hope it's help you

Answer 2

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