Question

Find the values of the following: sin 75°​

Answer 1

Answer:

sin 75°= (√3 + 1)/ 2√2

Step-by-step explanation:

Sin 75°​ we can write it as

Sin 75°​ = Sin(45°​+30°​)  

Applying the formula  

Sin (A + B) = Sin A. Cos B + Cos A. Sin B

So, Sin (45°​ + 30°​) = Sin 45°​. Cos 30°​ + Cos 45°​. Sin 30°​

We know that sin 45°​ =  1/√2

cos 30°​= √3/2

cos 45°​ =  1/√2

and sin 30°​ = 1/2

So,

Sin 45°​. Cos 30°​ + Cos 45°​. Sin 30°​ = 1/√2 . √3/2 + 1/√2 . 1/2

Sin (45°​ + 30°​)

SIn 75°​ = (√3 + 1) / 2√2