Question

Use the sum and difference formulas or a double angle formula to rewrite theexpressions as sin, cos or tana) cos^2x - 1/2 b) 6 sin x cos x

Answer 1

ANSWER

$cos^2x\text{ -}\frac{1}{2}\text{ = }\frac{1}{2}cos(2x)$$6\text{ sin x cos x = 3 sin \lparen2x\rparen}$

EXPLANATION

Given:

$\begin{gathered} 1).\text{ }cos^2x\text{ - }\frac{1}{2} \\ 2).\text{ 6 sin x cos x} \end{gathered}$

Desired Outcome:

Rewrite the expression as a sin, cos or tan using difference formulas or a double angle formula.

Double angle formula identities

$\begin{gathered} cos\text{ \lparen2x})\text{ = cos}^2x\text{ - sin}^2x\text{ .................equ 1} \\ cos\text{ \lparen2x\rparen = 2 cos}^2x\text{ - 1 .....................equ 2} \\ cos\text{ \lparen2x\rparen = 1 -2 sin}^2x\text{ ..........................equ 3} \end{gathered}$$sin\text{ \lparen2x\rparen= 2 sin x cos x ...............equ 4}$

Part A: Applying equation 2

$cos^2x\text{ - }\frac{1}{2}\text{ = }\frac{1}{2}cos\text{ \lparen2x\rparen}$

Part B: Applying equation 4

$6\text{ sin x cos x = 3 sin \lparen2x\rparen}$