Question

✔️Que - if sin 2x = root 2 cos x. Then x =?
✔️Que 2 - (tan A + tanB) /(cot A + cot B) is equal to?
PLS ANSWER FAST. BEST ANS WILL BE MARKED BRAINLIEST ✨ ✨.

Answer 1

here is the answer of question 2

Answer 2

Answer:

π/2, π/4, 3π/4

tanAtanB

Step-by-step explanation:

(1)

sin 2x = √2 cos x

⇒ 2sinxcosx = √2cosx

⇒ 2sinxcosx-√2cosx = 0

⇒ cosx(2sinx - √2) = 0

⇒ cosx=0, 2sinx - √2 = 0

(i)

cosx = 0

x = π/2.

(ii)

2sinx - √2 = 0

2sinx = √2

sinx = √2/2

sinx = 1/√2

x = π/4,3π/4

Therefore, x = π/2, π/4, 3π/4 (or) π/2 ± πn, π/4 ± πn, 3π/4 ± πn.

(2)

$Given:\frac{tanA+tanB}{cotA+cotB}$

$=\frac{tanA+tanB}{\frac{1}{tanA}+\frac{1}{tanB}}$

$=\frac{tanA+tanB}{\frac{tanA+tanB}{tanAtanB}}$

$=\frac{(tanA+tanB)(tanAtanB)}{tanA+tanB}$

$=\boxed{tanAtanB}$

Hope it helps!