How do you simplify tan4θ to trigonometric function of a unit θ ? Sub Grade: 10 - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

⇒

\tan 4 θ = \frac{4 tanθ - 4 ta n^{3} θ}{1 - 6 ta n^{2} θ + ta n^{4} θ}

Using the identity

\tan 2 θ = \frac{2 tanθ}{1 - ta n^{2} θ}

⇒

\tan 4 θ = \frac{2 \tan 2 θ}{1 - ta n^{2} (2 θ)}

⇒

\frac{2 x 2 tanθ}{\frac{1 - ta n^{2} θ}{(1 - \tan 2 θ)}} - \frac{4 ta n^{2} θ}{((1 - ta n^{2} θ))^{2}}

⇒

\frac{4 tanθ}{\frac{1 - ta n^{2} θ x (1 - ta n^{2} θ)^{2}}{(1 - ta n^{2} θ) - 4 ta n^{2} θ}}

⇒

\frac{4 tanθ (1 - ta n^{2} θ)}{(1 + ta n^{4} θ - 2 ta n^{2} θ - 4 ta n^{2} θ)}

⇒

\frac{4 tanθ - 4 ta n^{3} θ}{1 - 6 ta n^{2} θ + ta n^{4} θ}

.
Type Exam: CBSE

Related content