Question

sin-¹ (Sin-¹ ( 1/5) + cos-¹(x ) find x??​

Answer 1

Answer:

Given:-

$\sf \: sin\bigg( {sin}^{ - 1}\dfrac{x}{5} + {cos}^{ - 1} \dfrac{3}{5} \bigg)$

$\underbrace{\huge{ \pink{\underline{ \red{\sf \: To\:Find - }}}}}$

• $\sf \:\: Value \: of \:x$

$\underbrace{\huge \underline{ \red{\sf{Solution-}}}}$

$\underbrace{ \huge \red{ \underline{ \sf \: Given \: that - }}}$

$\rm :\longmapsto\: \sf \: sin\bigg( {sin}^{ - 1}\dfrac{x}{5} + {cos}^{ - 1} \dfrac{3}{5} \bigg) = 1:\\ \\ \rm :\longmapsto\: \sf \: {sin}^{ - 1}\dfrac{x}{5} + {cos}^{ - 1} \dfrac{3}{5} = {sin}^{ - 1}( 1):\\ \\ \rm :\longmapsto\: \sf \: {sin}^{ - 1}\dfrac{x}{5} + {cos}^{ - 1} \dfrac{3}{5} = {sin}^{ - 1}( sin\dfrac{\pi}{2} ):\\ \\ \rm :\longmapsto\: \sf \: {sin}^{ - 1}\dfrac{x}{5} + {cos}^{ - 1} \dfrac{3}{5} = \dfrac{\pi}{2}:\\ \\ \rm :\longmapsto\: \sf \: {sin}^{ - 1}\dfrac{x}{5} = \dfrac{\pi}{2} - {cos}^{ - 1} \dfrac{3}{5}:\\ \\ \rm :\longmapsto\: \sf \: {sin}^{ - 1}\dfrac{x}{5} = {sin}^{ - 1} \dfrac{3}{5}\\ \\ \: \: \: \: \: \: \because \: \bf \{ \: { \bf{ \: {sin}^{ - 1} x = \dfrac{\pi}{2} } \: - \: {cos}^{ - 1} x} \} \\ \\ \rm :\implies\:\dfrac{x}{ \cancel5} = \dfrac{3}{ \cancel5}$

$\bf\implies \underbrace \red{\underline{\:x \: = \:3}}$