Question

State true or false.

${\left(\tan x+\cot x\right)}^2={\sec }^{2}x+\cos e{c}^{2}x$

• A. True
• B. False

Answer 1

The correct option is A True

${(\tan x+\cot x)}^2={\tan }^{2}x+{\cot }^{2}x+2\tan x\cot x$

$={\tan }^{2}x+{\cot }^{2}x+2$

$={\sec }^{2}x-1+{cosec}^{2}x-1+2$

$={\sec }^{2}x+{cosec}^{2}x-2+2$

$={\sec }^{2}x+{cosec}^{2}x$

Hence the given statement is true.