Question

prove the above PlZ help or I will fail in my assingmentss​

Answer 1

Explanation:

Given that,

√( (1-sin∅)/(1+sin∅) ) = sec∅-tan∅

consider, LHS

√( (1-sin∅)/(1+sin∅) )

rationalise the denominator, we get

√( (1-sin∅)/(1+sin∅) × (1-sin∅)/(1-sin∅) )

⇒√( (1-sin∅)²/(1-sin²∅) )            (∵ (a-b)(a+b)=a²-b² )

⇒√( (1-sin∅)²/cos²∅ )               (∵ sin²∅+cos²∅=1⇒1-sin²∅=cos²∅)

⇒√( (1-sin∅)/cos∅ )²

⇒(1-sin∅)/cos∅

⇒1/cos∅ - sin∅/cos∅

⇒sec∅-tan∅ = RHS

∴Hence proved

HOPE THIS WOULD BE HELPFUL FOR YOU