Question

plzzz solve this fast ( question no.12)​

Answer 1

Note:

• tan(A+B) = (tanA + tanB) / (1 – tanA•tanB)

• tan(A–B) = (tanA – tanB) / (1 + tanA•tanB)

• tan2A = 2tanA / (1 – tan²A)

Solution:

To prove : tan50° = tan40° + 2tan10°

Proof :

We know that ;

tan(A–B) = (tanA – tanB) / (1 + tanA•tanB)

Thus,

Putting A = 50° and B = 40° in the above formula , we get ;

=> tan(50° - 40°)

= (tan50° - tan40°) / (1 + tan50°tan40°)

=> tan10°

= (tan50° - tan40°) / (1 + tan50°tan40°)

=> tan10°

= (tan50° - tan40°) / (1 + tan50°cot50°)

{ Since , tan∅ = cot (90°-∅)

Thus , tan40° = cot(90°-40°) = cot50° }

=> tan10°

= (tan50° - tan40°) / (1 + 1)

{ Since , cot∅ = 1/tan∅

Thus , tan∅cot∅ = 1 }

=> tan10° = (tan50° - tan40°) / 2

=> 2tan10° = tan50° - tan40

=> 2tan10° + tan40° = tan50°

=> tan50° = tan40° + 2tan10°

Hence Proved .

Answer 2

Answer is in the photo attached check it.. I hope it will help you!!!!!

PLEASE MARK AS BRAINLIEST!!