Verified Solution • 2025–26 Session moderate

QJEEM19Ma4daa: JEE Main 2019 Mathematics - Class 12 JEEM19Ma4daa Solution

The value of sin⁡−1(1213)−sin⁡−1(35){\sin ^{ - 1}}\left( {{{12} \over {13}}} \right) - {\sin ^{ - 1}}\left( {{3 \over 5}} \right) is equal to :

Multiple Choice Options

  • A π−sin⁡−1(6365)\pi - {\sin ^{ - 1}}\left( {{{63} \over {65}}} \right)
  • B π2−sin⁡−1(5665){\pi \over 2} - {\sin ^{ - 1}}\left( {{{56} \over {65}}} \right)
  • C π2−cos⁡−1(965){\pi \over 2} - {\cos ^{ - 1}}\left( {{9 \over {65}}} \right)
  • D π−cos⁡−1(3365)\pi - {\cos ^{ - 1}}\left( {{{33} \over {65}}} \right)

Step-by-Step Verified Solution

sin⁡−11213−sin⁡−135=sin⁡−1(1213.45.35.513){\sin ^{ - 1}}{{12} \over {13}} - {\sin ^{ - 1}}{3 \over 5} = {\sin ^{ - 1}}\left( {{{12} \over {13}}.{4 \over 5}.{3 \over 5}.{5 \over {13}}} \right)

⇒sin⁡−13365=π2−cos⁡−13365\Rightarrow {\sin ^{ - 1}}{{33} \over {65}} = {\pi \over 2} - {\cos ^{ - 1}}{{33} \over {65}}

⇒π2−sin⁡−15665\Rightarrow {\pi \over 2} - {\sin ^{ - 1}}{{56} \over {65}}

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