Question

Qno 25 pls solve that

Answer 1

Hey mate, here is your answer.....
Pls mark it as brainliest

Answer 2

Answer:

cosA+sinA

Step-by-step explanation:

Important Formulas:

(i) tanθ = sinθ/cosθ

(ii) cotθ = cosθ/sinθ

(iii) cosecθ = (1/sinθ)

(iv) secθ = (1/cosθ)

(v) sin²θ + cos²θ = 1

(vi) tan²θ - 1 = sec²θ

(vii) cot²θ - 1 = cosec²θ

(viii) a² - b² = (a + b)(a - b)

Now,

$Given:\frac{cosA}{1-tanA}+\frac{sinA}{1-cotA}$

$=\frac{cosA}{1-\frac{sinA}{cosA}}+\frac{sinA}{1-\frac{cosA}{sinA}}$

$=\frac{cosA}{\frac{cosA-sinA}{cosA}}+\frac{sinA}{\frac{sinA-cosA}{sinA} }$

$= \frac{cos^2A}{cosA-sinA}+\frac{sin^2A}{sinA-cosA}$

$=\frac{cos^2A}{cosA-sinA}-\frac{sin^2A}{cosA-sinA}$

$=\frac{cos^2A-sin^2A}{cosA-sinA}$

$=\frac{(cosA+sinA)(cosA-sinA)}{cosA-sinA}$

$=cosA+sinA$

Hope it helps!