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If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta?
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If √3 tan theta =3 sin theta , then find the value of sin^2 theta - co...
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If √3 tan theta =3 sin theta , then find the value of sin^2 theta - co...
Solution:
Given: √3 tan theta = 3 sin theta
We know that, tan theta = sin theta / cos theta
On substituting the value of tan theta, we get:
√3 * sin theta / cos theta = 3 sin theta
Multiplying both sides by cos theta, we get:
√3 sin theta = 3 sin theta cos theta
Dividing both sides by sin theta, we get:
√3 = 3 cos theta
Hence, cos theta = √3 / 3
Now, we can use the trigonometric identity sin^2 theta + cos^2 theta = 1 to find the value of sin^2 theta - cos^2 theta.
sin^2 theta + cos^2 theta = 1
sin^2 theta - cos^2 theta = 1 - 2cos^2 theta
Substituting the value of cos theta, we get:
sin^2 theta - cos^2 theta = 1 - 2(√3/3)^2
sin^2 theta - cos^2 theta = 1 - 2/3
sin^2 theta - cos^2 theta = 1/3
Therefore, the value of sin^2 theta - cos^2 theta is 1/3.
Hence, the solution.
Given: √3 tan theta = 3 sin theta
We know that, tan theta = sin theta / cos theta
On substituting the value of tan theta, we get:
√3 * sin theta / cos theta = 3 sin theta
Multiplying both sides by cos theta, we get:
√3 sin theta = 3 sin theta cos theta
Dividing both sides by sin theta, we get:
√3 = 3 cos theta
Hence, cos theta = √3 / 3
Now, we can use the trigonometric identity sin^2 theta + cos^2 theta = 1 to find the value of sin^2 theta - cos^2 theta.
sin^2 theta + cos^2 theta = 1
sin^2 theta - cos^2 theta = 1 - 2cos^2 theta
Substituting the value of cos theta, we get:
sin^2 theta - cos^2 theta = 1 - 2(√3/3)^2
sin^2 theta - cos^2 theta = 1 - 2/3
sin^2 theta - cos^2 theta = 1/3
Therefore, the value of sin^2 theta - cos^2 theta is 1/3.
Hence, the solution.
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If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta?.
If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If √3 tan theta =3 sin theta , then find the value of sin^2 theta - cos^2 theta?.
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