Question

.In ΔABC, if∠B = 90∘ and cot A = 1, then the value of cos C sin A – cos A sin C is *​

Answer 1

Answer:

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Answer 2

Answer:

The value of cosC sinA - cosA sinC = 0.

Step-by-step explanation:

Given:-

ABC is a right-triangle such that ∠B = 90° and cotA = 1.

To find:-

The value of cosC sinA - cosA sinC

According to the question,

It is given that ∠B = 90°. Then,

By the angle sum property,

∠A $+$ ∠B $+$ ∠C = 180°

∠A $+$ 90° $+$ ∠C = 180°

         ∠A $+$ ∠C = 180° - 90°

         ∠A $+$ ∠C = 90°

or, A $+$ C = 90° . . . . . (1)

Also,

Since cotA = 1

⇒ cosA/sinA = 1

⇒ cosA = sinA . . . . . (2)

Now,

Consider the expression as follows:

⇒ cosC sinA - cosA sinC

⇒ cosC cosA - SinA sinC (From (2))

Using the identity, cos(x + y) = cosx cosy - sinx siny, we get

⇒ cos(C + A)

⇒ cos (A + C)

⇒ cos90° (From (1))

⇒ 0

Therefore, the value of cosC sinA - cosA sinC is 0.

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