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The value of tan 20° × tan 40° × tan 80° is
- a)tan 30°
- b)tan 60°
- c)2 tan 30°
- d)2 tan 60°
Correct answer is option 'B'. Can you explain this answer?
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The value of tan 20° × tan 40° × tan 80° isa)t...
We know that tan 20 is not a special angle, so we cannot directly find its value. However, we can use the identity tan (90 - θ) = cot θ to find it.
tan (90 - 70) = cot 70
Now, we need to find the value of cot 70. We can use the identity cot θ = 1/tan θ to find it.
cot 70 = 1/tan 70
So, we need to find the value of tan 70. We can use the identity tan (90 - θ) = cot θ again to find it.
tan (90 - 20) = cot 20
Now, we need to find the value of cot 20. We can use the identity cot θ = 1/tan θ again to find it.
cot 20 = 1/tan 20
So, we have a circular equation. Let's solve it.
tan (90 - 70) = cot 70
tan (90 - 20) = cot 20
cot 70 = 1/tan 70
cot 20 = 1/tan 20
Substituting cot 70 and cot 20 in the first two equations, we get:
tan (90 - 70) = 1/tan 20
tan (90 - 20) = 1/tan 70
tan 20 = 1/tan (90 - 70)
tan 70 = 1/tan (90 - 20)
Using a calculator, we get:
tan 20 ≈ 0.36397
tan 70 ≈ 2.74748
Substituting these values in the last two equations, we get:
tan 20 ≈ 1/2.74748
tan 70 ≈ 1/0.36397
tan 20 ≈ 0.364
tan 70 ≈ 2.748
Therefore, the value of tan 20 is approximately 0.364.
tan (90 - 70) = cot 70
Now, we need to find the value of cot 70. We can use the identity cot θ = 1/tan θ to find it.
cot 70 = 1/tan 70
So, we need to find the value of tan 70. We can use the identity tan (90 - θ) = cot θ again to find it.
tan (90 - 20) = cot 20
Now, we need to find the value of cot 20. We can use the identity cot θ = 1/tan θ again to find it.
cot 20 = 1/tan 20
So, we have a circular equation. Let's solve it.
tan (90 - 70) = cot 70
tan (90 - 20) = cot 20
cot 70 = 1/tan 70
cot 20 = 1/tan 20
Substituting cot 70 and cot 20 in the first two equations, we get:
tan (90 - 70) = 1/tan 20
tan (90 - 20) = 1/tan 70
tan 20 = 1/tan (90 - 70)
tan 70 = 1/tan (90 - 20)
Using a calculator, we get:
tan 20 ≈ 0.36397
tan 70 ≈ 2.74748
Substituting these values in the last two equations, we get:
tan 20 ≈ 1/2.74748
tan 70 ≈ 1/0.36397
tan 20 ≈ 0.364
tan 70 ≈ 2.748
Therefore, the value of tan 20 is approximately 0.364.
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The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer?
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The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer?.
The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of tan 20° × tan 40° × tan 80° isa)tan30°b)tan 60°c)2 tan30°d)2tan 60°Correct answer is option 'B'. Can you explain this answer?.
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