Question

Sec theta - cos theta* cot theta +tan theta =tan theta*sec theta

Answer 1

using trigonometric identities..

hope this is helpful!!

Answer 2

To prove :

(sec θ - cos θ) × (cot θ + tan θ) = tan θ sec θ

Proof :

Taking LHS

→ LHS =  (sec θ - cos θ) × (cot θ + tan θ)

putting sec θ = 1 / cos θ  and  cot θ = 1 / tan θ

→ LHS = [(1/cos θ) - cos θ] × [(1/tan θ) + tan θ]

Taking LCM

→ LHS = [(1 - cos²θ)/cos θ] × [(1 + tan²θ)/tan θ]

using trigonometric identity : 1 - cos²θ = sin²θ  and  1 + tan²θ = sec²θ

→ LHS = ( sin²θ / cos θ ) × ( sec²θ / tan θ )

using sin θ / cos θ = tan θ

→ LHS = tan θ sin θ × ( sec²θ / tan θ )

→ LHS = sin θ sec²θ

Taking RHS

→ RHS = tan θ sec θ

putting tan θ = sin θ / cos θ

→ RHS = (sin θ / cos θ) sec θ

putting cos θ = 1 / sec θ

→ RHS = sin θ sec²θ

So,

LHS = RHS

Proved .