Question

prove that sin 75degree = √3+1/2√2
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Answer 1

Answer:

Step 1: Here, we can write Sin 75° as Sin (45°+30°) or Sin (30°+45°)

Step 2: So I take Sin (45°+30°)

Step 3: It is in the form of Sin(A+B) formula,

: ) Sin (A+B)=SinA.CosB + CosA.SinB

here A = 45°, B = 30° then

Step 4: According to Sin (A+B) formula,

=> Sin45°.Cos30°+Cos45°.Sin30°

=> (1 / √2).(√3 / 2)+(1 / √2).(1 / 2)

=> (√3 / 2√2) + (1 / 2√2)

Rationalize the denominator,

=> (√3+1/ 2√2) . (2√2 / 2√2)

=> (2√2.√3 + 2√2) / 4x2

=> (2√6 + 2√2) / 8

Take 2 as common,

=> 2 (√6 + √2) / 8

Therefore the resultant answer is

=> √6 + √2 / 4