Question

Prove tan(45+a)+tan(45-a)/tan(45+a)-tan(45-a)=cosec2a

Answer 1

Numerator :--

tan(45+A)+tan(45-A) =

= [tan(45)+tanA] / [1-tan45.tanA] + [tan(45)-tanA] / [1+tan45.tanA] =

= (1+tanA) / (1-tanA) + (1-tanA) / (1 + tanA)

= (1+tanA)² / (1-tan²A) + (1-tanA)² / (1 - tan²A)

= [(1+tanA)² + (1-tanA)²] / (1-tan²A)

= 2(1+tan²A) / (1-tan²A)

= 2sec2A

similarly ,

Denominator will become :-- 2tan2a

2sec2a/2tan2a = 1/sin2a = cosec2a [ proved]

Answer 2

Step-by-step explanation:

proof 10 45 + A + tan 45 minus 8 by 10 45 minus tan 45 minus is equal to cosec 2a ☹️⭐️✨✌️