Write the expression in terms of sine ans cosine and simplif

Write the expression in terms of sine ans cosine, and simplify so that no questions appear in the final expression. sin^2x + sin^21 x cot^2 x A) cot^2 x - 1 B) 1 C) sin^2 x + 1 D) cot^2 x + 1 Find the exact value of the expression using the provided information. Find tan(s - t) given that sin s = -3 squareroot 13/13, with s in quadrant IV, and sin t = - squareroot 10/10, with t in quadrant IV. A) -7/9 C) 11/3 C) -11/3 D) -11/9 Perform the indicated operations and simplify the result so there are no quotients. tan^2 theta - 3 sin theta tan theta sec theta A) 1 + cot theta B) sec theta csc theta C) sin theta tan theta D) -2 tan^2 theta Solve the equation for x, where x is restricted to the given interval. y = 8 cos 3x, for x in [0, pi/3]] A) x = 1/3 arccos y/8 B) x = 1/8 arccos y/3 C) x = 8 arccos y/3 D) x = 3 arccos y/8 Use a calculator to give the value to the nearest degree. theta = sin^-1(0.8830) A) 57 degree B)62 degree C) 60 degree D) 118 degree Write the product as a sum or difference of trigonometric functions. 2 sin 2x sin 12x A) cos 14x + cos 10x B) 1/2 (cos 14x + cos 10x) C) sin 14x + sin 10x D) cos 10x - cos 14x Find the exact value of the real number y. y = cos^-1(squareroot 2/2) A) pi/4 B) 11 pi/6 C) 7 pi/4 D) pi/6 Use identities to find the exact value. cos 165 degree A) - squareroot 6 - squareroot 2/4 B) squareroot 2 - squareroot 6/4 C) squareroot 6 - squareroot 2/4 D) squareroot 6 + squareroot 2/4

Solution

8. sin²x + sin²xcot²x

sin²x(1+cot²x)

and 1 + cot²x=csc²x

So we get

sin²x*csc²x= 1

9.sin s=-3sqrt13/13 =-3/sqrt13

cos s= 2/sqrt13

tan s= -3/2

sin t=-sqrt10/10=-1/sqrt10

cos t= 3/sqrt10

tan t= -1/3

tan(s-t)=(tans - tant)/(1+tan s tan t)= (-3/2 +1/3)/(1+(-3/2)(-1/3))

                                                  = (-7/6)/(9/6) = -7/9

10. tan²theta - 3sin theta tan theta sec theta

tan theta(tan theta - 3 sin theta sec theta)

And sin theta sec theta=tan theta

tan theta(tan theta-3tan theta)= tan theta(-2 tan theta)=-2tan²theta