Question

If sin A = `3/5 and cos B = 12/13`, evaluate:

tan A + tan B

Answer 1

Given

sin A = `3/5 and cos B = 12/13`

cos A = `sqrt(1 − sin^2 A)`

cos A = `sqrt (1 − (3/5)^2)`

cos A = `sqrt(1 −  9/25)`

cos A = `sqrt(16/25)`

cos A = `4/5`

tan A = `sin A/cos A`

tan A = `(3/5)/(4/5)`

tan A = `3/4`

sin B = `sqrt(1 − cos^2 B)`

sin B `sqrt(1 −  (12/13)^2)`

sin B = `sqrt(1 −  144/169)`

sin B = `sqrt 25/169`

sin B = `5/13`

tan B = `sin B/cos B`

tan B = `(5/13)/(12/13)`

tan B = 5/12

finally,

tan A + tan B = `3/4 + 5/12`

= `9/12 + 5/12`

= `14/12 = 7/6`

tan A + tan B = `7/6`