Question

prove :cos 40⁰ upon sin 50⁰ + sin 20⁰ upon cos 70⁰- tan 75 × tan 15 = 1

Answer 1

$\large\pink{\underline{\texttt{★ \: Formulas \: Used \: :-}}}$

$\large\blue{\texttt{ → \: Sin(90 - x) = Cos \: x}}$

$\large\blue{\texttt{ → \: Tan(90 - x) = Cot \: x}}$

$\large\blue{\texttt{ → \: Tan x = 1/Cot x}}$

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$\huge\red{\underline{\underline{\texttt{★ \: Solution\: :-}}}}$

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$\bf\pink{Taking \: L.H.S.}$

$\bf\green{ \frac{Cos \: 40⁰}{Sin \: 50°} + \frac{Sin \: 20°}{Cos \: 70°} - Tan \: 75° × Tan \: 15°}$

$\bf\green{ = \frac{Cos \: 40⁰}{Sin \: (90 - 40)°} + \frac{Sin \: 20°}{Cos \: (90 - 20)°} - Tan \: (90 - 15)° × Tan \: 15°}$

$\bf\green{ = \frac{Cos \: 40⁰}{Cos \: 40⁰} + \frac{Sin \: 20°}{Sin \: 20°} - Cot \: 15° × Tan \: 15°}$

$\bf\green{ = 1+ 1 - \frac {Cot \: 15° }{Cot \: 15°}}$

$\bf\green{ = 1+ 1 - 1}$

$\bf\green{ = 1}$

$\bf\pink{Which \: is \: equal \: to \: R.H.S.}$

$\bf\red{L.H.S.\: =\: R.H.S.}$

$\bf\red{Hence,\: Proved}$

Answer 2

Step-by-step explanation:

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