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

neela | High School Teacher | (Level 3) Valedictorian

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sina+cosa = 1

To find tan 2a .

We  put cosa = sqrt(1-sin^2a) in the given equation:

sina +sqrt(1-sin^2a) = 1

sqrt(1-sin^2a) = 1-sina.

Square both sides:

1-sin^2a = 1 -2sina +sin^2a

0 = -2sina + 2sin^2a

2sina(sina -1) = 0

sina = 0. Or sina = 1.

For sina = 0 , we get:a = 0. , or a = pi.

For sina = 1, a = 90 degree.

Therefore  , when a = 0 or pi,   tan2a = 0

When a = pi/2 or 90 degree,  tan2a = tan pi = 0

So  tan2a = 0.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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