Question

sin alpha = 3/5 and cos beta= 40/41, find value of : sin(alpha + beta) , cos(alpha -beta), tan (alpha +beta), cot(alpha-beta)​

Answer 1

Step-by-step explanation:

Hey Mate.....

given:

$\sin( \alpha ) = \frac{3}{5}$

$\cos( \beta ) = \frac{40}{41}$

for angle alpha

p=3,h=5&b=4(by Pythagoras theorem)

for beta angle

b=40,h=41&p=9(by Pythagoras theorem)

$\sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \sin( \beta ) \cos( \alpha )$

$= \frac{3}{5} \times \frac{40}{41} + \frac{9}{41} \times \frac{4}{5}$

$= \frac{120 + 36}{205}$

$= \frac{156}{205}$

others you can do same by the formulas

$\cos( \alpha - \beta ) = \cos( \alpha ) \cos( \beta ) + \sin( \alpha )sin( \beta )$

$\tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) }$

.......