If sin (A + B) = cos (A + B), what is the value of tan A?
Answer & explanation
Correct answer: option 1
According to question ,
sin (A + B) = cos (A + B)
by using formula
sin A cos B + cos A sin B = cos A cos B - sin A sin B
on rearranging ,
sin A cos B + sin A sin B = cos A cos B - cos A sin B
sin A(cos B + sin B) = cos A (cos B - sin B)
on rearranging ,
\(\frac{sinA}{cosA}\) = \(\frac{cos B - sin B}{cos B + sin B}\)
taking out common cosB from left hand side
tanA = \(\frac{1 - sin B / cosB}{1 + sin B/ cosB}\)
tan A = \(\frac{1 - tanB}{1+ tan B}\)