Question

Cos alpha/sin alpha=1/2, 1/cos beta=-5/3. Find tan(alpha+beta)

Answer 1

Step-by-step explanation:

cos alpha / sin alpha = 1/2. , so

sin alpha/ cos alpha = 2

tan alpha = sin alpha / cos alpha.

So tan alpha = 2

1/cos beta = -5/3

cos beta = -3/5

sin beta = √ 1- cos ^2 beta

sin beta = √1-(-3×-3/5×5)

= √1-9/25 = √25-9/25

sin beta = √ 16/25 = 4/5

tan beta = sin beta / cos beta

cos beta = -3/5 , sin beta = 4/5

tan beta =( 4/5 )/ (-3/5)

tan beta =-4/3

tan (alpha+beta) = tan alpha + tan beta / 1-tan alpha× tan beta.

={ 2 + (-4/3)}/1-2×(-4/3)

=(6 -4 /3 ) / 1+(8/3)

= (2/3 ) / 3+8/3

=(2/3) / 11/3

=2/3 × 3/11

tan (alpha + beta ) = 2/11

Hope it may help you ♥