Question

what is the value of ( 1+tan2O)+1+cot2O)​

Answer 1

Answer:

Explanation:

Given :

• (1 + tan²A)/(1 + cot²A)

To Find :

• The value of (1 + tan²A)/(1 + cot²A).

Solution :

(1 + tan²A)/(1 + cot²A)

• 1 + tan²A = sec²A
• 1 + cot²A = cosec²A

=> (sec²A)/(cos²A)

• sec²A = 1/cos²A
• cosec²A = 1/sec²A

=> (1/cos²A)/(1/sin²A)

=> (1/cos²A) × (sin²A/1)

=> (sin²A/cos²A)

• sin²A/cos²A = tan²A

=> tan²A

Hence :

• The value of (1 + tan²A)/(1 + cot²A) is tan²A.

Answer 2

$\bf\huge{\underline{\orange{Question↴}}}$

➥What is the value of

( 1+tan²A)+1+cot²A)

$\bf\huge{\underline{\orange{Answer↴}}}$

➥$\bf\dfrac{ (1 + tan²A) }{(1 + cot²A) }$

• 1 + tan²A = sec²A

• 1 + cot²A = cosec²A

➥ $\bf\dfrac{(sec²A) }{cos²A}$

• Sec²A = $\bf\dfrac{1}{cos²A}$

• Cosec²A = $\bf\dfrac{1}{sec²A}$

➥ ( $\bf\dfrac{1}{cos²A}$) ÷ ( $\bf\dfrac{1}{sin²A}$)

➥( $\bf\dfrac{1}{cos²A}$) × ( $\bf\dfrac{sin²A}{1}$)

➥ ($\bf\dfrac{sin²A}{cos²A}$)

• $\bf\dfrac{sin²A}{cos²A}$ = tan²A

➥ tan²A

$\bf{\bold{\orange{\therefore The~answer~is~tan²A}}}$