Trigonometric ratios of complementary angles: Class 10 practice
sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ, sec(90° − θ) = cosec θ. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Trigonometric ratios
The idea behind trigonometric ratios of complementary angles
sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ, sec(90° − θ) = cosec θ. Use them to simplify expressions like sin 37°/cos 53°.
Step-by-step method
- Check whether the two angles add to 90°.
- Rewrite one ratio using the complementary identity.
- Simplify.
Worked example 1 (Basic)
Evaluate sin 75° / cos 15°.
- cos 15° = sin 75°
- = 1
- Answer: 1
Worked example 2 (Standard)
Evaluate tan 43° × tan 47°.
- tan 47° = cot 43°
- tan × cot = 1
- Answer: 1
Worked example 3 (Challenge)
Evaluate 5 sin² 45° + 5 sin² 45°.
- sin 45° = cos 45°
- 5(sin² + cos²) = 5
- Answer: 5
Common mistakes and misconceptions
- Using it when angles don't add to 90°
- Pairing sin with sin
Practice questions
- (Basic) Evaluate sin 31° / cos 59°.
- (Basic) Evaluate sin 39° / cos 51°.
- (Standard) Evaluate tan 11° × tan 79°.
- (Standard) Evaluate tan 44° × tan 46°.
- (Challenge) Evaluate 2 sin² 15° + 2 sin² 75°.
- (Challenge) Evaluate 5 sin² 80° + 5 sin² 10°.
Answer key with full working
- Q1: cos 59° = sin 31° → = 1 → Answer: 1
- Q2: cos 51° = sin 39° → = 1 → Answer: 1
- Q3: tan 79° = cot 11° → tan × cot = 1 → Answer: 1
- Q4: tan 46° = cot 44° → tan × cot = 1 → Answer: 1
- Q5: sin 75° = cos 15° → 2(sin² + cos²) = 2 → Answer: 2
- Q6: sin 10° = cos 80° → 5(sin² + cos²) = 5 → Answer: 5
Syllabus note
This skill is listed under "Trigonometry" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is trigonometric ratios of complementary angles in?
"Trigonometry", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.