Question

Garry Tas : -tan 40°. tan 50°. sin 60º.cosec 60° = 1​

Answer 1

Answer:

Step-by-step explanation:

To Prove :-

$tan40\degree.tan50\degree.sin60\degree.cosec60\degree = 1$

Solution :-

Taking L.H.S :-

$tan40\degree.tan50\degree.sin60\degree.cosec60\degree$

We can write:- sinA = 1/cosecA

$= tan40\degree.tan50\degree.\dfrac{1}{cosec60\degree}.cosec60\degree$

$= tan40\degree\times tan50\degree$

We can write 40 = 90 - 50

$= tan(90-50)\times tan50\degree$

We know that tan(90 - A) = cotA

$= cot50\degree\times tan50\degree$

We know that, cotA = 1/tanA

$=\dfrac{1}{tan50\degree}\times tan50\degree$

= 1

= R.H.S

Since, L.H.S = R.H.S