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QJEEM19Ma4605: JEE Main 2019 Mathematics - Class 11 JEEM19Ma4605 Solution: If cos( + ) = 3/5 ,sin ( - ) = 5/13 and 0 < < , then tan(2 ) is …
If cos( + ) = 3/5 ,sin ( - ) = 5/13 and 0 < < , then tan(2 ) is equal to :
Multiple Choice Options
- A 21/16
- B 63/52
- C 33/52
- D 63/16
Step-by-Step Verified Solution
Given 0 < \alpha < {\pi \over 4}
and 0 < \beta < {\pi \over 4}
0 > - \beta > - {\pi \over 4}
0 < \alpha + \beta < {\pi \over 2}
and - {\pi \over 4} < \alpha - \beta < {\pi \over 4}
As cos( + ) = 3/5
so
As sin( - ) = 5/13
so
Now tan(2 ) = tan( + + - )
=
= =
and 0 < \beta < {\pi \over 4}
0 > - \beta > - {\pi \over 4}
0 < \alpha + \beta < {\pi \over 2}
and - {\pi \over 4} < \alpha - \beta < {\pi \over 4}
As cos( + ) = 3/5
so
As sin( - ) = 5/13
so
Now tan(2 ) = tan( + + - )
=
= =