Question

tan^2(x) × cos^2(x) = 1 - cos^2(x)

Answer 1

Answer:

true

Step-by-step explanation:

Answer 2

Answer: True

Step-by-step explanation:

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

$\mathrm{Manipulating\:left\:side}$

$\tan ^2\left(x\right)\cos ^2\left(x\right)$

$\mathrm{Use \ the \ basic \ trigonometric \ identity \ \:tan\left(x\right)=\frac{sin\left(x\right)}{cos\left(x\right)}}$

$=\cos ^2\left(x\right)\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2$

$=\frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}\cos ^2\left(x\right)$

$=\frac{\sin ^2\left(x\right)\cos ^2\left(x\right)}{\cos ^2\left(x\right)}$

$\mathrm{Cancel\:the\:common\:factor:}\:\cos ^2\left(x\right)$

$=\sin ^2\left(x\right)$

$\mathrm{Use \ the \ Pythagorean \ identity \ \cos ^2\left(x\right)-\sin ^2\left(x\right)=1 \rightarrow \sin ^2\left(x\right)=1-\cos ^2\left(x\right)}}$

$=1-\cos ^2\left(x\right)$

$1-\cos ^2\left(x\right) =1-\cos ^2\left(x\right)$

Left side = right side

Therefore, the identity is true