coseca-cota=2,find cosec^2a+cot^2a=?
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CoolestCat015
cosecA - cotA = 1/2 can be re - written as...
1/sinA - cosA/sinA=1/2
1 - cosA/sinA=1/2
2- 2cosA= sin A
cosA=2-sinA/2
use this
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Answer:-
Given:-
Cosec a - cot a = 2 -- equation (1)
We know that,
cosec² a - cot² a = 1
Using (a² - b²) = (a + b) (a - b) we get,
→ (Cosec a + cot a) (Cosec a - cot a) = 1
Substituting Cosec a - cot a = 2 from equation (1) we get,
→ (Cosec a + cot a) (2) = 1
→ Cosec a + cot a = 1/2 -- equation (2)
Adding equations (1) & (2) we get,
→ Cosec a - cot a + Cosec a + cot a = 2 + 1/2
→ 2cosec a = (4 + 1)/2
→ Cosec a = 5/2 * 1/2
→ Cosec a = 5/4
Putting the value of Cosec a in equation (1) we get,
→ 5/4 - cot a = 2
→ 5/4 - 2 = cot a
→ (5 - 8) / 4 = cot a
→ cot a = (- 3/4)
Hence,
cosec² a + cot² a = (5/4)² + ( - 3/4)²
→ cosec² a + cot² a = 25/16 + 9/16
→ cosec² a + cot² a = (25 + 9)/16
→ cosec² a + cot² a = 34/16
→ cosec² a + cot² a = 17/8
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