Question

Cos x(tan² x + 1) = sec x
Can anyone help me with this equation?

Answer 1

`\cos x \: ( { \tan}^(2) x \: + 1) = \sec x \: \: (proved)`

Explanation:

Equation provided:

• 
  `\cos x \: ( { \tan}^(2) x \: + 1) = \sec x`

To prove:

• LHS = RHS

Proof :

LHS -

`= \cos x \: ( { \tan}^(2) x \: + 1)`

• [As we know that tan^2 x + 1 = sec^2 x]

`= \cos \: x \: * {\sec }^(2) x`

• [Since cos x = 1/sec x]

`= (1)/( \sec \: x ) * {\sec }^(2) x`

`= \sec \: x`

RHS -

`= \sec \: x`

Hence,

LHS = RHS (Proved)