Find the exact value of y cos sin1 45 35 35 34 43 If sin th

Find the exact value of y = cos [(sin^-1 (-4/5))] 3/5 -3/5 3/4 -4/3 If sin theta = -12/13, and pi

Solution

7. y=cos(sin^-1(-4/5))

Let sin^-1(-4/5)=t

sin t=-4/5

Opposite=4 and hypotenuse=5

Therefore adjacent=sqrt(25-16)=3

cos t=adjacent/hypotenuse= 3/5

Therefore cos(sin^-1(-4/5))=3/5

8. sin theta=-12/13

opposite=12 hypotenuse=13

adjacent= sqrt(169-144)=5

In third quadrant cos is negative

cos theta=adjacent/hypotenuse -5/13

sec theta=1/cos theta=-13/5

Correct option is a

9.(sinx + cos x)²+(sinx - cosx)² = sin²x + cos²x+2sinx cos x+sin²x+cos²x-2sinxcosx

                                                 = 1+1=2

Correct option is b.

10. sin 53 cos 37 +cos 53 sin 37

This is of the form

sin(A+B)=sinA cos B+cos A sinB

sin(53+37)=sin 90=1

Hence the correct option is d