I need help with cd and e Suppose f know that sin x 45 and

I need help with c,d and e

Suppose f know that sin x = -4/5 and x in QIII. Use the above formulas to find sin 2x, cos 2x and tan 2x: (Don\'t use a calculator!) Suppose I know that cos(12degree) .2. Find cos^2 (6degree) - sin^2(6degree). (Don\'t use a calculator. use one of your above formulas) Simplify the expression: 2 sin 50 cos 50 (use one of your above formulas) Simplify the expression: 2 cos^2(4theta) - 1 (use one of your above formulas)

Solution

c) cos12 = 0.2 Find cos^2(6) -sin^2(6)

Formula we use : cos2x = cos^2x - sin^2x

So, cos12 = cos^2(6) - sin^2(6) = 0.2

So,cos^2(6) - sin^2(6) = 0.2

d) 2siin5theta*cos5theta

Use the formula : sin2x = 2sinx8cosx

So,2sin5theta*cos5theta = sin10theta

e) 2cos^2(4theta) -1

use the formula: cos2x = 2cos^2x -1

2cos^2(4theta) -1 = cos(2*4theta) = cos8theta