Prove that- ii 1cos -x-a cos -x-b - tan -x-b- tan- x-asin -a-b

Solution: To nbsp;Prove : nbsp;1cos ⁡(x−a) nbsp; nbsp;cos ⁡(x−b) = tan ⁡(x−b) tan⁡ (x−a)sin ⁡(a−b) R.H.S. tan ⁡(x−b) tan ⁡(x−a)sin⁡(a−b) nbsp; ...

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Trigonometric Ratios for Sum of Two Angles

Prove that: i...

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Prove that: $(i i)$ $\frac{1}{cos (x - a) cos (x - b)} = \frac{tan (x - b) - tan (x - a)}{sin (a - b)}$

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\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c

{(a^{- 1} + b^{- 1})}^{- 1} = \frac{a b}{a + b}

\tan A = \frac{5}{6} and \tan B = \frac{1}{11}

A + B = \frac{π}{4}

\tan A = \frac{m}{m - 1} and \tan B = \frac{1}{2 m - 1}

A - B = \frac{π}{4}

Prove that:

(i) $\frac{a + b + c}{a^{- 1} b^{- 1} + b^{- 1} c^{- 1} + c^{- 1} a^{- 1}} = a b c$

(ii) $(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

(i i)

\frac{1}{sin (x - a) cos (x - b)} = \frac{cot (x - a) + tan (x - b)}{cos (a - b)}

tan x + tan (x + \frac{π}{3}) + tan (x + \frac{2 π}{3}) = 3,

\frac{3 tan x - {tan}^{3} x}{1 - 3 {tan}^{2} x} = 1.

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