Question

6. If tan A + cot A = 2, then find the value of
tan²A + cot²A.

(2016-PZ8S1LO)

Unique question asked by CBSE in 2016-PZ8S1LO

The one who will give help to me I will mark his / her answer as brainlist answer​

Answer 1

Answer :-

Value of tan² A + cot² A is 2.

Explanation :-

tan A + cot A = 2

Squaring on both sides

⇒ ( tan A + cot A )² = ( 2 )²

⇒ tan² A + cot² A + 2tan A. cot A = 4

[ ∵ ( x + y )² = x² + y² + 2xy ]

⇒ tan² A + cot² A + 2tan A . ( 1 / tan A ) = 4

[ ∵ cot A = 1 / tan A ]

⇒ tan² A + cot² A + 2 ( 1 ) = 4

⇒ tan² A + cot² A + 2 = 4

⇒ tan² A + cot² A = 4 - 2

⇒ tan² A + cot² A = 2

∴ the value of tan² A + cot² A is 2.

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

tanA + cotA = 2

Here we have to Squaring both sides :-

(tanA + cotA)² = (2)²

${\boxed{\sf\:{Identity=(a + b)^2 = a^2+ b^2+ 2ab}}}$

tan² A + cot² A + 2tan A × cot A = 4

Identity :-

$\tt{\rightarrow cotA=\dfrac{1}{tanA}}$

$\tt{\rightarrow tan^2A+cot^2A+2tanA\times\dfrac{1}{tanA}=4}$

tan² A + cot² A + 2(1) = 4

tan²A + cot²A + 2 = 4

tan²A + cot²A = 4 - 2

tan²A + cot²A = 2

Hence we get :-

tan²A + cot²A = 2

$\boxed{\begin{minipage}{11 cm} Fundamental Trignometric Indentities \\ \\ \sin^{2}\theta+\cos^{2}\theta =1 \\ \\ 1+tan^{2}\theta=\sec^{2}\theta \\ \\ 1 + cot^{2}\theta=\text{cosec}^2\theta \\ \\ tan\theta =\dfrac{sin\theta}{cos\theta} \\ \\ cot\theta =\dfrac{cos\theta}{sin\theta} \end{minipage}}$