MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Trigonometric Ratios for Sum of Two Angles

The general s...

Question

The general solution of the equation $tan θ + tan 4 θ + tan 7 θ = tan θ tan 4 θ tan 7 θ$ is

Open in App

Solution

We know that, $tan (θ + 4 θ + 7 θ)$

$= \frac{t a n (θ + 4 θ) + t a n 7 θ}{1 - t a n (θ + 4 θ) t a n 7 θ}$

$= \frac{\frac{t a n θ + t a n 4 θ}{1 - t a n θ t a n 4 θ} + t a n 7 θ}{1 - t a n θ + t a n 4 θ 1 - t a n θ + t a n 4 θ + t a n 7 θ}$

$= \frac{t a n θ + t a n 4 θ + t a n 7 θ - t a n θ t a n 4 θ t a n θ}{1 - t a n θ t a n 4 θ - t a n θ + t a n 4 θ + t a n 7 θ - t a n θ t a n 4 θ t a n 7 θ}$

$t a n 12 θ = \frac{t a n θ + t a n 4 θ + t a n 7 θ - t a n θ t a n 4 θ t a n 7 θ}{1 - t a n θ + t a n 4 θ + t a n 7 θ - t a n θ t a n 4 θ - t a n θ t a n 4 θ t a n 7 θ}$

We know that $t a n θ + t a n 4 θ + t a n 7 θ = t a n θ 4 θ t a n 7 θ$

$\Rightarrow t a n 12 θ$ = $\frac{t a n θ t a n 4 θ t a n 7 θ - t a n θ t a n 4 θ t a n 7 θ}{1 - t a n θ + t a n 4 θ + t a n 7 θ - t a n θ t a n 4 θ - t a n θ - t a n 4 θ - t a n 7 θ}$

$\Rightarrow tan 12 θ = 0$

$\Rightarrow tan 12 θ = 0$

$\Rightarrow 12 θ = n π$

$\Rightarrow θ = n π / 12$

Suggest Corrections

thumbs-up

0

Similar questions

Q. General solution of

tan θ + tan 4 θ + tan 7 θ = tan θ tan 4 θ tan 7 θ

tan θ + tan 4 θ + tan 7 θ = tan θ tan 4 θ tan 7 θ

, then the general solution is?

tan θ + tan 4 θ + tan 7 θ = tan θ tan 4 θ tan 7 θ

A solution of $tan θ + tan 4 θ + tan 7 θ = tan θ tan 4 θ tan 7 θ$ is given by $(n \in Z)$

Q. The general solution of the equation

{tan}^{4} θ - 1 = 2^{{tan}^{2} θ}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Trigonometric Ratios for Sum of Two Angles

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon