Question

in triangle ABC angle B =90degrees.if cotA =1/√3 then find the value of cos A.cosC-sinA.sinC​

Answer 1

Answer

0

$\rule{200}1$

Explanation

Since, ΔABc has ∠B = 90°, the other two angles, viz, ∠A and ∠C will be acute angles such that

∠A = 90° - ∠C

Given, cotA = 1/√3

⇒ cotA = cot60°

⇒ ∠A = 60° (We directly compared the angles because we know that ∠A is acute)

⇒ ∠C = 90° - ∠A = 90° - 60° = 30°

⇒ cosA = cos60° = 1/2

⇒ cosC = cos30° = √3/2

⇒ sinA = sin60°= √3/2

⇒ sinC = sin30° = 1/2

⇒ cosAcosC - sinAsinC

= (1/2)(√3/2) - (√3/2)(1/2)

= √3/4 - √3/4

= 0

Answer 2

Answer:0

Step-by-step explanation: