Question

Find the value of: sin $75\textdegree$

Answer 1

We can also write sin 75° as sin (45+30)°

Using the formula sin(a+b)°=sina°.cosb° + cosa°.sinb°

=sin45°.cos30° + cos45°.sin30°

sin45°=cos45°=1/√2, sin30°=1/2, cos30°=√3/2

=(1/√2).(√3/2) + (1/√2).(1/2)

=2/(√2*3) + 1/(2√2)

=2*√6/(√6.√6) + √2/(2√2*√2)

=2√6/6 + √2/(2*2)

=√6/3 + √2/4

=(√6*4 + √2*3)/12

Hence,(4√6 + 3√2)/12 is the required value of sin75°.

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