Question

convert sin A to cot A​

Answer 1

Answer:

$sin \: a \: = 1 \div cosec \: a$

$putting \: the \: value \: of \: cosec \: a$

$sin \: a \: = \: 1 \div \sqrt{1 + cot {}^{2} \: a }$

Answer 2

Answer- The above question is from the chapter 'Introduction to Trigonometry'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Trigonometric Identities:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Given question: Convert sin A to cot A​.

Solution: We know that  cosec²θ - cot²θ = 1.

$\dfrac{1}{sin^{2} A} + cot^{2} A = 1\\\\\dfrac{1}{sin^{2} A} = 1 - cot^{2} A\\\\sin^{2} A = \dfrac{1}{1 - cot^{2} A}\\\\sin A = \sqrt{\dfrac{1}{1 - cot^{2} A}}$

$sin A = \dfrac{1}{\sqrt{1 \: - cot^{2} A}}$

∴ sin A in terms of cot A = $\dfrac{1}{\sqrt{1 \: - cot^{2} A}}$