Question

How do you verify a trig identity algebraically?

Answer 1

Using Pythagoras Theorem.....

Answer 2

Is that all?

Answer 3

Should I complete this? wait!!!

Answer 4

In triangle ABC \[\angle C = 90^0\]
Hence it is a right angled triangle
Here \[\sin \theta = \frac{AB}{AC}\]
\[\cos \theta = \frac{BC}{AC}\]
By using Pythagoras theorem
\[AC^2 = AB^2 + BC^2\]
Dividing both sides by \[AC^2\] we find;
\[\frac{AC^2}{AC^2} = \frac{AB^2}{AC^2} + \frac{BC^2}{AC^2}\]
\[1=( \frac{AB}{AC})^2 + (\frac{BC}{AC})^2\]
\[1=( \sin \theta)^2 + (\cos \theta)^2\]
\[\rightarrow 1=\sin^2 \theta + \cos^2 \theta\]
that is
\[\sin^2 \theta + \cos^2 \theta=1\]
This is the first trigonometric identity
similarly we can prove \[1 + \tan^2 \theta = \sec^2 \theta\]
and \[1 + \cot^2 \theta = cosec^2 \theta\] by diivding both sides by \[BC^2 \] and \[AB^2 \] RESPECTIVELY.
@girlover

Answer 5

Omg ty

Answer 6

DID YOU GET?