Question

Prove that.
Sin x tan x / 1- cos x= 1+ sec x

Answer 1

Hey there !!!!

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We can even prove it by using RHS

= 1+secx

= 1+1/cosx

= (cosx+1)/cosx

Multiplying and dividing with 1-cosx

= (1+cosx)(1-cosx)/cosx(1-cosx)

= (1-cos²x)/cosx(1-cosx)

But sin²x+cos²x=1

So 1-cos²x=sin²x

= sin²x/cosx(1-cosx)

= sinx*sinx/cosx(1-cosx)

= sinxtanx/(1-cosx)

LHS=RHS

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Hope this helped you.............

Answer 2

Concept:

The trigonometry values are used to measure the angles and sides of a right-angle triangle. The other side of the representation of trigonometric values formulas are:

Tan θ = sin θ/cos θ

Cot θ = cos θ/sin θ

Sin θ = tan θ/sec θ

Cos θ = sin θ/tan θ

Sec θ = tan θ/sin θ

Cosec θ = sec θ/tan θ

Sin²x= 1- Cos²x

Given:

We have given the equation: Sin x tan x / 1- Cos x= 1+ sec x

Find:

We have to prove : Sin x tan x / 1- Cos x= 1+ sec x

Solution:

Given Equation: Sin x tan x / 1- Cos x

We know that: Sin²x= 1- Cos²x

Let's solve the equation:

LHS

Sin x tan x / 1 - Cos x

= Sin x Sin x / Cos x (1- Cos x)

= Sin²x / Cos x (1- Cos x)

= 1 - Cos² x / Cos x (1 - Cos x)

= ( 1 + Cos x) / Cos x

= 1 + Sec x

= RHS

LHS= RHS

Hence, Sin x tan x / 1- Cos x= 1+ sec x

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