Question

Tan^2(x) × cos^2(x) = 1 - cos^2(x)

Answer 1

true

Explanation:

Answer 2

Answer: True

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)=(sin\left(x\right))/(cos\left(x\right))}`

`=\cos ^2\left(x\right)\left((\sin \left(x\right))/(\cos \left(x\right))\right)^2`

`=(\sin ^2\left(x\right))/(\cos ^2\left(x\right))\cos ^2\left(x\right)`

`=(\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