Trig identities: sin²A + cos²A = 1
The trig identities are sin²A + cos²A = 1, 1 + tan²A = sec²A, 1 + cot²A = cosec²A.
What each letter means
- \(A\) an acute angle of a right triangle (Class 10); any angle from Class 11
- \(\sin^2A\) means (sin A)²
When to use it
To find cos θ or tan θ from sin θ (or the other way round), to simplify expressions, and to turn a trig equation into one with a single trig function.
Worked example
If \(\sin A=\tfrac35\) and \(A\) is acute, find \(\sec A+\tan A\).
- \(\cos A=\sqrt{1-\tfrac{9}{25}}=\tfrac45\)
- \(\sec A=\tfrac54,\ \tan A=\tfrac{3/5}{4/5}=\tfrac34\)
Answer: \(\sec A+\tan A=2\)
Common mistake
Forgetting the sign. sin²θ + cos²θ = 1 gives cos θ = ±√(1 − sin²θ): choose the sign from the quadrant.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
| Class 11 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
Questions
What is the trig identities formula?
The trig identities are sin²A + cos²A = 1, 1 + tan²A = sec²A, 1 + cot²A = cosec²A. A: an acute angle of a right triangle (Class 10); any angle from Class 11; sin²A: means (sin A)².
Is the trig identities given in the exam?
Class 10: learn it: CBSE gives no formula booklet. Class 11: learn it: CBSE gives no formula booklet. This comes from our own CBSE Maths formula sheets; your teacher has the official booklet.
Where does sin²θ + cos²θ = 1 come from?
A point at angle θ on the unit circle is (cos θ, sin θ). Pythagoras on the radius, which has length 1, gives cos²θ + sin²θ = 1.
Our own wording, examples and card, checked by CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.