Given the real number a calculate tan2a if sina cosa 1Solu

Given the real number a calculate tan2a if sina + cosa = 1

Solution

We\'ll square raise the given relation sina + cosa = 1.

(sina + cosa)^2 = 1^2

(sina)^2 + (cosa)^2 + 2sina*cosa = 1 (1)

But, from the fundamental formula of trigonometry:

(sina)^2 + (cosa)^2 = 1

We\'ll substitute (sina)^2 + (cosa)^2 by 1:

The relation (1) will become:

1 + 2sina*cosa = 1

We\'ll eliminate like terms:

2sina*cosa = 0

But 2sina*cosa = sin (2a)

We\'ll write the formula for tan 2a:

tan 2a = sin 2a/cos 2a

tan 2a = 0/cos 2a

tan 2a = 0