Tough Trigonometric Identities Test - 23+ MCQs: Trigonometric Identities Quiz: Test Your Understanding with Essential Identity Questions and Answers

1. What is the product-to-sum identity for sine?

sin(theta)sin(phi) = 1/2[cos(theta - phi) - cos(theta + phi)]

sin(theta)sin(phi) = 1/2[cos(theta + phi) + cos(theta - phi)]

sin(theta)sin(phi) = 1/2[sin(theta + phi) - sin(theta - phi)]

sin(theta)sin(phi) = 1/2[sin(theta - phi) + sin(theta + phi)]

2. What is the double-angle identity for cosine?

cos(2theta) = cos^2(theta) - sin^2(theta)

cos(2theta) = 2cos^2(theta) - 1

cos(2theta) = 1 - 2sin^2(theta)

cos(2theta) = 2sin^2(theta) - 1

3. What is the reciprocal identity for cosine?

csc(theta) = 1/sin(theta)

sec(theta) = 1/cos(theta)

cot(theta) = 1/tan(theta)

cos(theta) = 1/sin(theta)

4. Which identity involves both sine and cosine?

tan(theta) = sin(theta)/cos(theta)

cot(theta) = cos(theta)/sin(theta)

sin(2theta) = 2sin(theta)cos(theta)

cot(2theta) = cot^2(theta) - 1

5. Prove the identity: cos²(x) - sin²(x) = 1

Use the Pythagorean identity

Apply double-angle formulas

Use the quotient identity

Apply the sum-to-product formula

6. What is the sum-to-product identity for cotangent?

cot(theta)cot(phi) = tan((theta + phi)/2)/1 - tan((theta + phi)/2)

cot(theta)cot(phi) = cot((theta + phi)/2)/1 + cot((theta + phi)/2)

cot(theta)cot(phi) = sin(theta + phi)/cos(theta + phi)

cot(theta)cot(phi) = 1/2[cot(theta + phi) + cot(theta - phi)]

7. Which identity is known as the Power-Reducing or Half-Angle identity?

cos^2(theta) = (1 + cos(2theta))/2

sin^2(theta) = (1 - cos(2theta))/2

tan^2(theta) = (1 - cos(2theta))/(1 + cos(2theta))

cot^2(theta) = (1 + cos(2theta))/sin^2(theta)

8. What is the double-angle identity for sine?

sin(2theta) = 2sin(theta)cos(theta)

sin^2(theta) = 1 - cos^2(theta)

cos(2theta) = cos^2(theta) - sin^2(theta)

cot(2theta) = cot^2(theta) - 1

9. What is the half-angle identity for tangent?

tan(theta/2) = sin(theta)/1 + cos(theta)

tan(theta/2) = sin(theta)/1 - cos(theta)

tan(theta/2) = 1 - cos(theta)/sin(theta)

tan(theta/2) = 1 + cos(theta)/sin(theta)

10. What is the co-function identity for sine?

sin(pi/2 - theta) = cos(theta)

sin(2theta) = 2sin(theta)cos(theta)

sin(theta) = tan(theta)/cot(theta)

sin(theta) = 1/csc(theta)

Trigonometric Identities MCQ Test 2