Maths Inverse Trigonometric Functions Inverse Trigonometric Functions Class 12th Ncert Solutions Maths class 12th

41. $c o s^{- 1} \frac{12}{13} + s i n^{- 1} \frac{3}{5} = s i n^{- 1} \frac{56}{65}$

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Vishal Baghel | Contributor-Level 10

8 months ago

$c o s^{- 1} \frac{12}{13} + s i n^{- 1} \frac{3}{5} = s i n^{- 1} \frac{56}{65}$

Let $c o s^{- 1} \frac{12}{13} = xandsin^{- 1} \frac{3}{5} = y .$

Thin, $c o s x = \frac{12}{13} and sin y = \frac{3}{5}$

Using $s i n (x + y) = s i n x c o s y + c o s x s i n y .$

$s i n [c o s^{- 1} \frac{12}{13} + s i n^{- 1} \frac{3}{5}] = \frac{5}{13} * \frac{4}{5} + \frac{12}{13} * \frac{3}{5} = \frac{20 + 36}{65} = \frac{56}{65} .$

$c o s^{- 1} \frac{12}{13} + s i n^{- 1} \frac{3}{5} = s i n^{- 1} \frac{56}{65} .$

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