Question

prove the identity.

\\\tan x \left(1 - \sin^2 x\
ight) = \frac{1}{2} \sin 2x\\

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statement
\\\tan x \left(1 - \sin^2 x\
ight)\\

reason
select
algebraic transformation
reciprocal identities
quotient identities
pythagorean identities
odd and even identities
double-angle identities
sum and difference identities

Explanation:

Apply the Pythagorean identity

Using the Pythagorean Identities and Trigonometric Proofs knowledge points

$$
LATEXBLOCK0
$$

Apply the quotient identity

Using the Trigonometric Proofs knowledge point

$$
LATEXBLOCK1
$$

Apply the double-angle identity

Using the Trigonometric Proofs knowledge point

$$
LATEXBLOCK2
$$

Answer:

To complete the first step of proving the identity:

$$\tan x (1 - \sin^2 x) = \tan x \cos^2 x$$

Reason: Pythagorean identities