Question

Prove That : (tan theta + sec theta -1)(tan theta + sec theta +1)=2 sin theta/1 - sin theta

Answer 1

tan@ + sec@ – 1 = (sin@ – cos@ + 1)/cos@
tan@ + sec@ + 1 = (sin@ + cos@ + 1) / cos@

Answer 2

Concept

The process of measuring angles relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that can be derived from these three fundamental ratios or functions.

Given

(tanθ ₊ secθ ₋ 1)(tanθ ₊ secθ ₊ 1) = 2sinθ / 1₋sin²θ

Find

we need to prove the above given expression.

Solution

L.H.S = (tanθ ₊ secθ ₋ 1)(tanθ ₊ secθ ₊ 1)

multiply the above terms.

= tan²θ ₊ tanθsecθ ₊ tanθ ₊ secθtanθ ₊ sec²θ ₊ secθ ₋ tanθ ₋ secθ ₋ 1

cancelling like terms.

= tan²θ ₊ tanθsecθ ₊ sec²θ ₊ secθtanθ

= tan²θ ₊ sec²θ ₊ 2 tanθsecθ ₋ 1

using the identity tan²θ ₊ sec²θ = 1

= 1 ₊ 2 tanθsecθ ₋ 1

=  2 tanθsecθ

= 2 sinθ/cosθ × 1/cosθ

= 2sinθ/cos²θ

= 2sinθ/1₋sin²θ

= R.H.S

hence, proved

#SPJ2

your question was incomplete. Please find the missing content below.

prove that : (tanθ ₊ secθ ₋ 1)(tanθ ₊ secθ ₊ 1) = 2sinθ / 1₋sin²θ