Find tan sin1 45 3pi2 Only basic mathematical operators pow

Find tan [sin^-1 (-4/5) - 3pi/2]. (Only basic mathematical operators, powers, and square roots are allowed in this answer box. Trig functions are not allowed. For example, if the answer is squareroot 3/2, then you must enter sqrt(3)/2; you cannot enter cos(pi/6).) Your Answer: Correct Answer: 3/4

Solution

tan[ sin^-1(-4/5) -3pi/2 ]

let x = sin^-1(-4/5)

So, tan[x -3pi/2] = -tan[3pi/2 -x]

= -tan[ pi + (pi/2 -x)]

=- tan[ pi/2 -x]

= -cotx

x = sin^-1(-4/5)

sinx = -4/5 ; tanx = -4/3 ----> cotx = -3/4

= -(-3/4) = 3/4

tan[ sin^-1(-4/5) -3pi/2 ] = 3/4