Question

a) Prove that
sin(105°) = ( sqrt(6) + sqrt(2) ) / 4

Answer 1

Step-by-step explanation:

Given:-

Sin 105°

To find:-

Prove that :-

Sin 105° = (√6+√2)/4

Solution:-

Given that

Sin 105°

It can be written as Sin (60°+45°)

It is in the form of Sin (A+B)

Where , A = 60° and B = 45°

We know that

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

On Substituting these values of A and B in the above formula,then

=> Sin (60°+45°)

=> Sin 60° Cos 45° + Cos 60°° Sin 45°

=> (√3/2) × (1/√2) + (1/2) × (1/√2)

=> (√3×1)/(2×√2) + (1×1)/(2×√2)

=> (√3/2√2 )+(1/2√2)

=>(√3+1)/2√2

On multiplying both numerator and the denominator with √2 then

=> [√2](√3+1)/(2√2×√2)

=>[ (√2×√3)+(√2×1)] / (2×√2×√2)

=> (√6 + √2) / (2×2)

=> (√6 + √2)/4

Sin 105° = (√6 + √2) / 4

Hence, Proved.

Used formula:-

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