Question

Q1.iF THETA IS A POSITIVE ACUTE ANGLE AND TAN 3 THETA = COT(60- THETA), THEN FIND THE VALUE OF SIN 3 THETA, PLS HELP I NEED IT RIGHT NOW I WILL MARK BRRAINLIEST

Answer 1

Step-by-step explanation:

SOLUTION

GIVEN

θ is positive acute angle and

tan 3θ = cot ( 60° - θ )

TO DETERMINE

The value of θ

EVALUATION

Here it is given that θ is positive acute angle and tan 3θ = cot ( 60° - θ )

Now

tan 3θ = cot ( 60° - θ )

⇒ cot ( 90° - 3θ ) = cot ( 60° - θ )

⇒ ( 90° - 3θ ) = ( 60° - θ )

⇒ - 3θ + θ = 60° - 90°

⇒ - 2θ = - 30°

⇒ θ = 15°

FINAL ANSWER

θ = 15°

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Answer 2

Answer:

Given:

tan2θ tan3θ = 1

Concept used:

1/tanθ = cotθ

cotθ = tan(90o - θ )

Calculation:

tan2θ tan3θ = 1

⇒ tan3θ = 1/tan2θ

⇒ tan3θ = cot2θ

⇒ tan3θ = tan(90o - 2θ)

⇒ 3θ = 90 - 2θ

⇒ 5θ = 90o

⇒ θ = 18o

Hence, The value of θ is 18o.

⇒ tanAtanB = 1

⇒ A + B = 90o

Then,

⇒ 2θ + 3θ = 90o

⇒ 5θ = 90o

⇒ θ = 18o

Hence, The value of θ is 18o