Prove the following:

Let, sin-¹ = x & cot-¹ = y

sin x = & cot y =

As, sin x = 3/5 ⇒ tan x = 3/4 {using basic t-ratios}

And cot y = 3/2 ⇒ tan y = 2/3

∴ tan-¹(3/4) = x & tan-¹(2/3) = y

⇒ sin-¹ + cot-¹ = tan-¹ + tan-¹

⇒ sin-¹ + cot-¹ = {∵ tan^-1x + tan^-1y = tan^-1

⇒ sin-¹ + cot-¹ = …eq(1)

∴ LHS = cos (sin-¹ + cot-¹)

⇒ LHS = cos () {from equation 1}

Let, = z (say)

∴ LHS = cos z

Now we need to find the value of cos z to prove the given equation

∵

⇒ {using basic t-ratios}

Using the LHS from the given equation,

LHS = RHS