Question

In triangle abc right angled at c if tana =1 by root3 and tanb = root3 show that sina.cosb+ cosa .sinb =1

Answer 1

Step-by-step explanation:

Here,

In triangle ABC right angled at C if tanA = 1/√3 and tanB = √3

Then,

tanA = 1/√3 = BC/AC

And, tanB = √3 = AC/BC

Using Pythagoras Theorem,

AB= √(BC²+AC²)

= √{1²+(√3)²}

= √(1+3)

= √4

= 2

Now,

LHS = sinA . cosB + cosA . sinB

= BC/AB . BC/AB + AC/AB . AC/AB

= BC²/AB² + AC²/AB²

= BC²+AC²

AB²

= AB²/AB²

= 1

= RHS

OR,

LHS = sinA . cosB + cosA . sinB

= BC/AB . BC/AB + AC/AB . AC/AB

= BC²/AB² + AC²/AB²

= 1²/2² + (√3)²/2²

= 1/4 + 3/4

= (1+3)/4

= 4/4

= 1