Question

if cot theta +tan theta=2 then prove:cot²theta +tan²theta=2​

Answer 1

Step-by-step explanation:

cot theta + tan theta = 2

squaring on both sides

(cot theta + tan theta)^2 = 4

cot^2 theta + tan^2 theta + 2×tan theta×cot theta =4

we know that, tan theta×cot theta = 1

cot^2 theta + tan ^2 theta +2 = 4

cot^2 theta +tan^2 theta = 2

Hence proved!

Answer 2

Answer:

Proof

Step-by-step explanation:

cot∅ = $\frac{1}{tan∅}$

$\frac{1}{tan∅}$ + tan∅ = 2

$\frac{1+tan\\^{2} ∅}{tan ∅}$ = 2

1+ tan²∅ = 2tan∅

tan²-2tan∅+1 = 0

(tan∅-1)²=0

So, tan∅ - 1 = 0

  tan∅ = 1

Hence cot∅ =  $\frac{1}{tan∅}$ = 1/1 = 1

tan²∅=1²=1

cot²∅=1²=1

Hence cot²∅+tan²∅=1+1 = 2