HELP WITH TRIG, EQUATIONS, SOLVE FOR X

Question

Answer 1

2.1)

Step 1:

The trigonometric identity is

Consider LHS is

Trigonometric properties are

Substitute formulas in LHS and simplify.

Solution:

Answer 2

2.2)

The trigonometric expression is

Rewrite the identity is

Sum of trigonometric identity :

Answer 3

2.3)

The values of acute triangle

Find the value of

Difference of trigonometric identity :

Rewrite the angle is

Substitute above values in

Answer 4

2.4)

The expression is  

Simplify.