Prove that 1-2x-2xwhere x- n- n - I

Solving LHS, we get 1+^2x 1+cos^2xsin^2x cos^2x+sin^2xsin^2x 1sin^2x ^2x #160; = RHS,Hence proved ...

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Implicit Differentiation

Prove that ...

Question

Prove that $1 + {cot}^{2} x = {csc}^{2} x$
where $x \neq n π, n ϵ I$

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1 + {tan}^{2} x = {sec}^{2} x

x \neq (2 n + 1) \frac{π}{2}, n ϵ I

\frac{tan 3 x - tan 1 x}{1 + tan 3 x tan 1 x} = 1

x = \frac{n π}{2} + \frac{π}{8}, n ϵ I

tan α = 1

α = n π + \frac{π}{4}, n ϵ I .

Prove $x = n π + (- 1)^{n} . \frac{π}{2}$ or $x = (n π + \frac{3 π}{4})$ , where m, $n \in I$

Prove $x = \frac{n π}{2}$ or $x = (\frac{m π}{2} + \frac{3 π}{8})$ , where m, $n \in I$

x

y

\frac{π}{2}

tan x = tan y \Rightarrow x = n π + y

n \in z

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