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zzz [600]
1 year ago
8

option 1 drop down are: even-odd identity, quotient identity, Pythagorean identity, double-number identity.option 2 drop down ar

e: combine like terms, even-odd identities, definition of subtraction, cofunction identity.option 3 drop down are: double-number identity, cofunction identity, Pythagorean identity, even-odd identity.

Mathematics
1 answer:
motikmotik1 year ago
5 0

Answer:

The equation is given below as

\frac{\cos2x}{\cos x}=\cos x-\sin x\tan x

Step 1:

We will work on the left-hand side, we will have

\begin{gathered} \cos x-\sin x\tan x \\ \text{recall that,} \\ Quoitent\text{ identity is} \\ \tan x=\frac{\sin x}{\cos x} \end{gathered}

By substituting the identity above, we will have

\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x}=\cos x-\frac{\sin^2x}{\cos x} \\  \end{gathered}

Here, we will make use of the quotient identity

Step 2:

By writings an expression, we will have

\begin{gathered} \cos x-\sin x\tan x=\cos x-\frac{\sin x.\sin x}{\cos x} \\ \cos x-\sin x\tan x=\frac{\cos^2x-\sin^2x}{\cos x} \end{gathered}

Here, we will use the definition of subtraction

\cos x-\frac{\sin^2x}{\cos x}

Step 3:

We will apply the double number identity given below

\begin{gathered} \cos 2\theta=\cos (\theta+\theta)=\cos ^2\theta-\sin ^2\theta \\ \cos 2x=cos(x+x)=\cos ^2x-\sin ^2x \end{gathered}

By applying this, we will have

\frac{\cos^2x-\sin^2x}{\cos x}=\frac{\cos2x}{\cos x}

Here, we will use the double number identity

\frac{\cos^2x-\sin^2x}{\cos x}

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