Question

if tan Q + 1/tan Q =2 then find value of tan^2Q+1/tan^2 Q​

Answer 1

Answér :

tan²Q + 1/tan²Q = 2

Solution :

• Given : tanQ + 1/tanQ = 2
• To find : tan²Q + 1/tan²Q = ?

We have ;

tanQ + 1/tanQ = 2

Now ,

Squaring both the sides , we have ;

=> (tanQ + 1/tanQ)² = 2²

=> (tanQ)² + (1/tanQ)² + 2tanQ•(1/tanQ) = 4

=> tan²Q + 1/tan²Q + 2 = 4

=> tan²Q + 1/tan²Q = 4 - 2

=> tan²Q + 1/tan²Q = 2

Hence ,

tan²Q + 1/tan²Q = 2 .

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

Alternative method :

We have ,

=> tanQ + 1/tanQ = 2

=> (tan²Q + 1)/tanQ = 2

=> tan²Q + 1 = 2tanQ

=> tan²Q - 2tanQ + 1 = 0

=> (tanQ)² - 2×tanQ×1 + 1² = 0

=> (tanQ - 1)² = 0

=> tanQ - 1 = 0

=> tanQ = 1

=> tanQ = tan45°

=> Q = 45°

Now ,

=> tan²Q + 1/tan²Q = tan²45° + 1/tan²45°

=> tan²Q + 1/tan²Q = 1² + 1/1²

=> tan²Q + 1/tan²Q = 1 + 1

=> tan²Q + 1/tan²Q = 2

Hence ,

tan²Q + 1/tan²Q = 2 .