How do you simplify sin(sin^-1( 3/5) + tan^-1( 7/24))?

1 Answer
P dilip_k
Apr 16, 2016

=4/5

Explanation:

=sin(sin^-!(3/5)+cot^-1(24/7))
=sin(sin^-!(3/5)+csc^-1sqrt(1+(24/7)^2))
=sin(sin^-!(3/5)+csc^-1(25/7))
=sin(sin^-!(3/5)+sin^-1(7/25))

=sinsin^-!(3/5)cossin^-1(7/25)+cossin^-!(3/5)sin sin^-1(7/25))
=(3/5)coscos^-1sqrt(1-(7/25)^2)+cosscos^-1sqrt(1-(3/5)^2)sin sin^-1(7/25)
=3/5xx24/25+4/5xx7/25=100/125=4/5

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