Question

Find the least values of the tan ^2 x + cot^2 x

Answer 1

Answer:search in ncert book

Answer 2

AnswEr:

GivEn:

• tan²x + cot²x

To Find:

• Find the least values of the tan²x + cot²x

Solution:

tan²x + cot²x

$\\ \implies\huge{\sf{ \dfrac{sin^2 x}{cos^2 x} + \dfrac{ cos^2 x}{sin^2 x} }} \\ \\ \\ \implies\huge{\sf{ \dfrac{sin^4 x + cos^4 x}{cos^2 x sin^2 x} }} \\ \\ \\ \implies\huge{\sf{ \dfrac{(sin^2x - cos^2x)^2 + 2 sin^2 x cos^2 x}{cos^2 \: x \: sin^2 x } }}$

$\implies\huge\orange{\boxed{\sf{ [ \dfrac{sin^2 x - cos^2 x}{ cos x sin x} ]^2 + 2 \geq \: 2 }}}$

Following Identities:

• $\bullet{\boxed{\sf{ tan \theta = \dfrac{sin \theta}{cos \theta} }}}$

• $\bullet{\boxed{\sf{ cot \theta = \dfrac{cos \theta}{sin \theta} }}}$

• $\bullet{\boxed{\sf{ sec \theta = \dfrac{1}{cos \theta} }}}$

• $\bullet{\boxed{\sf{ Cosec \theta = \dfrac{1}{sin \theta} }}}$

$\sf\underline\pink{Trigonometry:-}$ The Branch of mathematics which deals with the study of properties of triangles.