Assertion (A): If sec θ + tan θ = p, then sec θ = Reason (R): sec2 θ − tan2 θ = 1 1. A is true, R is false 2. A is false, R is true 3. Both A and R are true 4. Both A and R are false

Question

KnowledgeBoat · Accepted Answer

Given, sec θ + tan θ = p We know that, sec2 θ − tan2 θ = 1 (sec θ + tan θ)(sec θ − tan θ) = 1 (p)(sec θ − tan θ) = 1 sec θ − tan θ = Add sec θ + tan θ and sec θ − tan θ, sec θ + tan θ + sec θ − tan θ = p + 2sec θ = sec θ = Assertion (A) is false. sec2 θ − tan2 θ = 1 is a standard Pythagorean Identity. Reason is true. A is false, R is true Hence, option 2 is the correct option.

Mathematics

Assertion (A): If sec θ + tan θ = p, then sec θ = Reason (R): sec2 θ − tan2 θ = 1 1. A is true, R is false 2. A is false, R is true 3. Both A and R are true 4. Both A and R are false

Trigonometric Identities

Related Questions

Assertion (A): (1 − cosec² θ)(1 − sec² θ) = 1
Reason (R): 1 + tan² θ = sec² θ and 1 + cot² θ = cosec² θ
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false

Assertion (A): For an acute angle θ, if sin θ = cos θ, then 2 sin² θ + tan² θ = 1
Reason (R): For any acute angle θ, sin (90° − θ) = cos (45° + θ)
A is true, R is false
A is false, R is true
Both A and R are true
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Mathematics

Assertion (A): If sec θ + tan θ = p, then sec θ = Reason (R): sec2 θ − tan2 θ = 1 1. A is true, R is false 2. A is false, R is true 3. Both A and R are true 4. Both A and R are false

Trigonometric Identities

Related Questions

Assertion (A): (1 − cosec2 θ)(1 − sec2 θ) = 1Reason (R): 1 + tan2 θ = sec2 θ and 1 + cot2 θ = cosec2 θA is true, R is falseA is false, R is trueBoth A and R are trueBoth A and R are false

Assertion (A): For an acute angle θ, if sin θ = cos θ, then 2 sin2 θ + tan2 θ = 1Reason (R): For any acute angle θ, sin (90° − θ) = cos (45° + θ)A is true, R is falseA is false, R is trueBoth A and R are trueBoth A and R are false

Assertion (A): (1 − cosec² θ)(1 − sec² θ) = 1
Reason (R): 1 + tan² θ = sec² θ and 1 + cot² θ = cosec² θ
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false

Assertion (A): For an acute angle θ, if sin θ = cos θ, then 2 sin² θ + tan² θ = 1
Reason (R): For any acute angle θ, sin (90° − θ) = cos (45° + θ)
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false