tancos1 sqrt32 sin1 35 find the exact valueSolutionlet 1 c

tan(cos^1 sqrt3/2 - sin^-1 (-3/5)) find the exact value

let @1 = cos^-1 ( 3^1/2 / 2)

cos(@1) = 3^1/2 / 2

cos@1 = cos30

@1 = 30 degree

let @2 = sin^-1(-3/5)

sin(@2) = - 3/5

cos@2 = ( 1- sin²(@2)) ^1/2 (sin²@ + cos²@ = 1)

= ( 1 - ( -3/5)² ) ^1/2

cos(@2) = 4/5

so given question will be , tan(@1 - @2) = ?

tan( @1 - @2) = sin( @1 - @2) / cos(@1 - @2) ---------------------------1

sin(@1 - @2) = sin@1* cos@2 - cos@1 *sin@2

= sin30* ( 4/5) - cos30 * ( -3/5)

= (1/2)* (4/5) + ( 3^1/2 /2)* (3/5)

= 0.919

cos(@1 - @2) = cos@1 *cos@2 + sin@1*sin@2

= cos30 * (4/5) + sin30* (-3/5)

= 0.392

so from eq 1, tan(@1 - @2) = 0.919 / 0.392

= 2.34