Question

If cot????=3/4, prove that √sec????-cosec????/sec????+cosec????=1/√7

Answer 1

Answer:

please mention proper question

Answer 2

√(secθ-cosecθ)/(secθ+cosecθ) = 1/√7  proved

Step-by-step explanation:

Given: Cotθ = 3/4

To prove: prove that √(secθ-cosecθ)/(secθ+cosecθ) = 1/√7

Solution:  

 Cotθ = 3/4 = Adjacent / Opposite  

So Hypotenuse = √(4² + 3² = √(16 + 9) = √25 = 5

Now Cotθ = 3/4

Secθ = hypotenuse / Adjacent = 5/3

Cosecθ = hypotenuse / opposite = 5/4

So LHS √(secθ-cosecθ)/(secθ+cosecθ) = √ (5/3 - 5/4) / (5/3 + 5/4)

 = √ (20 - 15)/12 / (20 +15)12

 = √5/35

 = √1/7

 = 1/√7

 LHS = RHS

Hence proved.