Question

5. If tan A + cot A = 2,(A is an acute angle) the value of tanỪA + cot?A=
1
a. 0.
b. 1.
C. 4.
d. 2​

Answer 1

Answer:

your ans=A=45°

Step-by-step explanation:

$\sf\ \: tanA + cotA = 2 \\ \\ \sf\ \implies: tanA + \frac{1}{tanA} = 2 \\ \\ \sf\ \implies: \frac{ {tanA}^{2} + 1}{tanA} = 2\\ \\ \sf\ \implies: {tanA}^{2} + 1 = 2 tanA \\ \\ \sf\ \implies: {tanA}^{2} + {1}^{2} - 2 \times \: tanA \times 1 \\ \\\sf\ \implies: {(tanA - 1)}^{2} = 0 \\ \\ \sf\ \implies: (tanA - 1) = \sqrt{0} \\ \\ \sf\ \implies: (tanA - 1) = 0 \\ \\ \sf\ \implies: tanA = 1 \\ \\ \sf\ \implies:tanA = tan45 \degree \\ \\ \sf\boxed{ \implies: A = 45 \degree} \\ \\ \tt\ \: tan 45\degree + cot45 \degree = 1 + 1 = 2$