If tan + cot = 7, then find the value of tan2 + cot2 .
Answers
Answer:
Required numeric value of tan^2 A + cot^2 A is 47.
Step-by-step explanation:
Given,
tanA + cotA = 7
Square on both sides :
= > ( tanA + cotA )^2 = 7^2
From the properties of expansion :
- ( a + b )^2 = a^2 + b^2 + 2ab
= > ( tanA )^2 + ( cotA )^2 + 2tanAcotA = 49
= > tan^2 A + cot^2 A + 2tanA( 1 / tanA ) = 49 { cotA = 1 / tanA }
= > tan^2 A + cot^2 A + 2( 1 ) = 49
= > tan^2 A + cot^2 A + 2 = 49
= > tan^2 A + cot^2 A = 47
Hence the required numeric value of tan^2 A + cot^2 A is 47.
Answer:
tan²A + cot²A = 47.
Step-by-step explanation:
Given,
➾ tanA + cotA = 7
Squaring on both sides :
( tanA + cotA )² = 7²
∴ [ (a + b)² = a² + b² + 2ab ]
➾( tan² A + cot² A + 2 tanA ∙ cotA ) = 49
∴ [ cotA = 1/ tanA ]
➾ tan² A + cot² A + 2 tanA ∙ 1/tanA = 49
➾ tan² A + cot² A + 2 = 49
➾ tan² A + cot² A = 49 - 2
➾ tan² A + cot² A = 47