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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

If A, B, C are in arithmetic progression and B = (π)/(4), then tan...

If A,B,CA, B, C are in arithmetic progression and B=π4,B = \dfrac{\pi}{4}, then tanAtanBtanC=tan Atan Btan C =

Correct answer

1

Step-by-step solution

∵∵ Angles A,B,CA, B, C are in arithmetic progression and ∠B=π4∠ B = \dfrac{\pi}{4}

then {A=π4−θC=π4+θ\begin{cases}A = \dfrac{\pi}{4} - \theta & C = \dfrac{\pi}{4} + \theta\end{cases}

Hence tan⁡(π4−θ)tanπ4tan⁡(π4+θ)\tan \left(\dfrac{\pi}{4} - \theta\right)tan \dfrac{\pi}{4}\tan \left(\dfrac{\pi}{4} + \theta\right)

=1−tanθ1+tanθ.1.1+tanθ1−tanθ= \dfrac{1 - tan \theta}{1 + tan \theta} . 1 . \dfrac{1 + tan \theta}{1 - tan \theta}

=1= 1
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