If sin β is the harmonic mean of sin α and cos α , and sin θ is the arithmetic mean of sin α and cos α , then which of the following is/are correct? [ 2018 − II ] 1) 2 sin ( α + 4 π ) sin β = sin 2 α 2) 2 sin θ = cos ( α − 4 π ) Select the correct answer using the code given below:

Question

If sin β is the harmonic mean of sin α and cos α , and sin θ is the arithmetic mean of sin α and cos α , then which of the following is/are correct? [ 2018 − II ] 1) 2 ​ sin ( α + 4 π ​ ) sin β = sin 2 α 2) 2 ​ sin θ = cos ( α − 4 π ​ ) Select the correct answer using the code given below:, 1 only, 2 only, Both 1 and 2, Neither 1 nor 2

MARKS App · Accepted Answer

From question, sin α , sin β and cos α are in H . P then, sin β = s i n α + c o s α 2 s i n α c o s α ​ and sin α , sin θ and cos α are in A.P. then, 2 sin θ = sin α + cos α Statement 1: 2 ​ sin ( α + 4 π ​ ) ⋅ sin β = ( sin α + cos α ) ⋅ s i n α + c o s α 2 s i n α c o s α ​ = 2 sin α cos α = sin 2 α Statement 2 : cos ( α − 4 π ​ ) = 2 ​ 1 ​ ( sin α + cos α ) = 2 ​ 2 s i n θ ​ = 2 ​ sin θ

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