Question

Show that Csc2x+csc4x+csc8x+csc16x+csc32x=cotx-cot32x

Answer 1

we have to prove that,

cosec2x + cosec4x + cosec8x + cosec16x + cosec32x = cotx - cot32x

proof : we have to use a trigonometric application, cotθ - cot2θ = cosec2θ

so, cosec2x = cotx - cot2x

cosec4x = cot2x - cot4x

cosec8x = cot4x - cot8x

cosec16x = cot8x - cot16x

cosec32x = cot16x - cot32x

now LHS = cosec2x + cosec4x + cosec8x + cosec16x + cosec32x

= (cotx - cot2x ) + (cot2x - cot4x ) + (cot4x - cot8x ) + (cot8x - cot16x ) + (cot16x - cot32x )

= cotx - cot32x = RHS

hence proved

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Answer 2

Step-by-step explanation:

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