Question

1. If TanX=CotY then prove that X+Y=90°​

Answer 1

Answer:

If x +y = 90° and sin x : sin y = √3: 1, then what is the ratio x: y?

we are given x+y=90∘ and sin x: sin y=3–√:1

We need to find the ratio of x:y

x+y=90∘

⇒y=90∘−x __________(1)

We are also given sinxsiny=3√1

⇒sinxsin90−x=3√1

⇒sinxcosx=3√1

⇒tanx=3–√

⇒x=60∘

Putting the value of x in eqn 1, we get

y=30∘

∴xy=6030

⇒x:y=2:1