Question

find the exact value of the sin (a-b), if sin a= 12/13 and sin b = 5/13. and b are between 0 and pi/2.
how can i get the value of cos a and cos b??????

Answer 1

\[\large cosa = \sqrt{1 - \sin^2a}\]

Answer 2

The same for is to find cosb..

Answer 3

But there you will include sinb in the square root brackets..

Answer 4

First one for cosa I am doing for cosb you will do:

\[\large cosa = \sqrt{1 - \frac{144}{169}} \implies \sqrt{\frac{25}{169}} \implies \color{green}{cosa= \frac{5}{13}}\]

Answer 5

Now find for cosb and after this use:

\[\large \sin(a - b) = sina \cdot cosb - cosa \cdot sinb\]

Answer 6

ok. i got it! thank you!

Answer 7

Welcome dear..