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tan⁻1(1/4)+ tan⁻1(2/9) is equal to
- a)(1/2)cos⁻1(3/5)
- b)(1/2)sin⁻1(3/5)
- c)(1/2)tan⁻1(3/5)
- d)tan⁻1(1/2)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b...
Solution:
We know that tan(A+B) = (tanA + tanB) / (1-tanA tanB)
Using the above formula, we can write:
tan(1/4 + 2/9) = (tan1/4 + tan2/9) / (1-tan1/4 tan2/9)
Let's find the values of tan(1/4) and tan(2/9) using the formula:
tan(2x) = 2tanx / (1-tan^2x)
tan(1/2) = 2tan(1/4) / (1-tan^2(1/4))
Solving the above equation, we get:
tan(1/4) = (2-sqrt(2)) / (2+sqrt(2))
Similarly, we can find the value of tan(2/9) as:
tan(2/9) = (2-tan(1/4)) / (1+2tan(1/4))
Substituting the values of tan(1/4) and tan(2/9) in the above equation, we get:
tan(1/4 + 2/9) = (tan1/4 + tan2/9) / (1-tan1/4 tan2/9)
tan(17/36) = [(2-sqrt(2))/(2+sqrt(2))] + [(2-(2-sqrt(2))/(2+sqrt(2)))] / [1-((2-sqrt(2))/(2+sqrt(2)))((2-(2-sqrt(2))/(2+sqrt(2))))]
Simplifying the above equation, we get:
tan(17/36) = 1/2
Using the formula, tan2x = 2tanx / (1-tan^2x), we can find the value of tan(1/2) as:
tan(1/2) = 2tan(1/4) / (1-tan^2(1/4))
Substituting the value of tan(1/4), we get:
tan(1/2) = [2((2-sqrt(2))/(2+sqrt(2)))] / [1-((2-sqrt(2))/(2+sqrt(2)))^2]
Simplifying the above equation, we get:
tan(1/2) = 1/2
Hence, the given expression tan(1/4) * tan(2/9) is equal to:
tan(1/4) * tan(2/9) = tan(1/4 + 2/9) - tan(1/2)
Substituting the values of tan(1/4 + 2/9) and tan(1/2), we get:
tan(1/4) * tan(2/9) = 1/2 - 1/2
tan(1/4) * tan(2/9) = 0
Therefore, the correct option is 'D', i.e. tan(1/4) * tan(2/9) is equal to tan(1/2).
We know that tan(A+B) = (tanA + tanB) / (1-tanA tanB)
Using the above formula, we can write:
tan(1/4 + 2/9) = (tan1/4 + tan2/9) / (1-tan1/4 tan2/9)
Let's find the values of tan(1/4) and tan(2/9) using the formula:
tan(2x) = 2tanx / (1-tan^2x)
tan(1/2) = 2tan(1/4) / (1-tan^2(1/4))
Solving the above equation, we get:
tan(1/4) = (2-sqrt(2)) / (2+sqrt(2))
Similarly, we can find the value of tan(2/9) as:
tan(2/9) = (2-tan(1/4)) / (1+2tan(1/4))
Substituting the values of tan(1/4) and tan(2/9) in the above equation, we get:
tan(1/4 + 2/9) = (tan1/4 + tan2/9) / (1-tan1/4 tan2/9)
tan(17/36) = [(2-sqrt(2))/(2+sqrt(2))] + [(2-(2-sqrt(2))/(2+sqrt(2)))] / [1-((2-sqrt(2))/(2+sqrt(2)))((2-(2-sqrt(2))/(2+sqrt(2))))]
Simplifying the above equation, we get:
tan(17/36) = 1/2
Using the formula, tan2x = 2tanx / (1-tan^2x), we can find the value of tan(1/2) as:
tan(1/2) = 2tan(1/4) / (1-tan^2(1/4))
Substituting the value of tan(1/4), we get:
tan(1/2) = [2((2-sqrt(2))/(2+sqrt(2)))] / [1-((2-sqrt(2))/(2+sqrt(2)))^2]
Simplifying the above equation, we get:
tan(1/2) = 1/2
Hence, the given expression tan(1/4) * tan(2/9) is equal to:
tan(1/4) * tan(2/9) = tan(1/4 + 2/9) - tan(1/2)
Substituting the values of tan(1/4 + 2/9) and tan(1/2), we get:
tan(1/4) * tan(2/9) = 1/2 - 1/2
tan(1/4) * tan(2/9) = 0
Therefore, the correct option is 'D', i.e. tan(1/4) * tan(2/9) is equal to tan(1/2).
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Community Answer
tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b...
By the formula ,
tan^-1(x) + tan^-1(y) = tan^-1 (x+y)/1-xy
when comparing ,
x= 1/4 and y= 2/9
substitute the values of x and y in the formula to get the answer
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tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b)(1/2)sin⁻1(3/5)c)(1/2)tan⁻1(3/5)d)tan⁻1(1/2)Correct answer is option 'D'. Can you explain this answer?
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tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b)(1/2)sin⁻1(3/5)c)(1/2)tan⁻1(3/5)d)tan⁻1(1/2)Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b)(1/2)sin⁻1(3/5)c)(1/2)tan⁻1(3/5)d)tan⁻1(1/2)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for tan⁻1(1/4)+ tan⁻1(2/9) is equal toa)(1/2)cos⁻1(3/5)b)(1/2)sin⁻1(3/5)c)(1/2)tan⁻1(3/5)d)tan⁻1(1/2)Correct answer is option 'D'. Can you explain this answer?.
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