Question

Express cosA in
terms of sin A/2​

Answer 1

✽ Question ✽

Express cos A in terms of sin A/2.

✽ To find ✽

cos A in terms of sin A/2.

✽ Solution ✽

For all values of the angle A we know that,

cos 2A

= 1 - 2 sin² A or 1 - cos 2A

= 2 sin² A

To express cosA in terms of sin A/2, we have to replace A by A/2 in the above relation.

So,

cos A

= 1 - 2 sin² A/2 or 1 - cos A

= 2 sin² A/2

✽ Hence ✽

cos A

= 1 - 2 sin² A/2 or 1 - cos A

= 2 sin² A/2

✽ Therefore ✽

cos A when expressed in sin A/2 is

2 sin² A/2.

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✽ Know more ✽

• Express sin A in terms of A/2 →

For all values of the angle A we know that,

sin 2A = 2 sin A cos A

To express sin A in terms of A/2, we have to replace A by A/2 in the above relation.

So,

sin A = 2 sin A/2 cos A/2

• Express tan A in terms of A/2 →

For all values of the angle A we know that, tan 2A = (2 tan A)/(1 – tan² A)

To express tan A in terms of A/2, we have to replace A by A/2 in the above relation.

So,

tan A = (2tan A/2)/(1−tan² A/2)

◎ Hope this helps you. ◎