Question -
Answer -
(i) Given sin (sin-1 7/25)
Now let y = sin-1 7/25
Sin y = 7/25 where y ∈ [0, π/2]
Substituting thesevalues in sin (sin-1 7/25) we get
Sin (sin-1 7/25)= 7/25
(ii) Given Sin (cos-1 5/13)
(iii) Given Sin (tan-1 24/7)
(iv) Given Sin (sec-1 17/8)
(v) Given Cosec (cos-1 8/17)
Let cos-1(8/17)= y
cos y = 8/17 where y ∈ [0, π/2]
Now, we have to find
Cosec (cos-1 8/17)= cosec y
We know that,
sin2 θ+ cos2 θ = 1
sin2 θ= √ (1 – cos2 θ)
So,
sin y = √ (1 – cos2 y)
= √ (1 – (8/17)2)
= √ (1 – 64/289)
= √ (289 – 64/289)
= √ (225/289)
= 15/17
Hence,
Cosec y = 1/sin y = 1/(15/17) = 17/15
Therefore,
Cosec (cos-1 8/17)= 17/15
(vi) Given Sec (sin-1 12/13)
(vii) Given Tan (cos-1 8/17)
(viii) Given cot (cos-1 3/5)
(ix) Given Cos (tan-1 24/7)
