Trigonometric Identity Proofs Worksheet
Prove trigonometric identities using fundamental identities, algebraic manipulation, and various proof techniques.
Includes
Standards
Topics
Trigonometric Identity Proofs
Name:
Date:
Score:
Prove the following trigonometric identities. Show all your steps clearly. Use fundamental identities, algebraic manipulation, and any other valid proof techniques.
1. Prove the identity: (sin θ + cos θ)² = 1 + 2sin θ cos θ
2. Complete the steps to prove the identity: tan x + cot x = sec x csc x
tan x + cot x = (sin x / cos x) + (cos x / )
= (sin² x + cos² x) / (cos x )
= 1 / (cos x sin x)
= (1 / cos x) * (1 / )
= sec x
3. Prove the identity: (1 - cos² θ) / sin θ = sin θ
4. Which of the following is equivalent to (sec² x - 1) / tan x?
sin x
cos x
tan x
cot x
5. The identity sin² θ + cos² θ = 1 is known as the Pythagorean identity.
True
False
6. Prove the identity: (1 + tan² x) / (1 + cot² x) = tan² x
Related Worksheets
Radian Measure Worksheet
This worksheet focuses on understanding and converting between radian and degree measures, and applying radian measure to arc length and sector area problems.
Angle of Elevation and Depression Worksheet
Explore angle of elevation and depression with real-world problems involving trigonometry for grade 9 students.
Trigonometric Functions Worksheet
Explore trigonometric functions, ratios, and their applications in right-angled triangles for Grade 9 mathematics.