Question

If sin A = 1/√3, then find the value of...
cosec²A-sec²A/cosec²A+cot²A

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Answer 1

Q.If sin A = 1/√3, then find the value of...

cosec²A-sec²A/cosec²A+cot²A

answer:sin A = 1313 Now we will construct a triangle ABC in which ∠B = 90° and BC : AC = 1 : 3 Let BC = k and AC = 3k where k > 0 which is a constant quantityRead more on Sarthaks.com - https://www.sarthaks.com/788741/if-sin-a-1-3-then-find-the-value-of-cos-a-cosec-a-tan-a-sec-a

Answer 2

$\huge\mathcal\red{Question}$

If sin A = 1/√3, then find the value of...

cosec²A-sec²A/cosec²A+cot²A

$\huge\mathcal\red{Answer}$

sin A = 1/3

Now we will construct a triangle ABC in which ∠B = 90° and BC : AC = 1 : 3 ,

Let BC = k and AC = 3k ,

where k > 0 which is a constant quantity.

→From Budhayana formula

→AC²=AB²- BC²

→AB²=AC²- BC²

→AB²=(3k)²- (k)²

→AB²=9k²- k² = 8k²

→AB²=±2√2

$→$

since ∠A is acute there fore AB will be +ve

$→$

CosA =

$\frac{AB}{BC} = \frac{2 \sqrt{2k} }{3k} = \frac{ 2\sqrt{2} }{3}$

→ cossec A = 3

→ TanA =

$\frac{BC}{AB} = \frac{k}{ 2\sqrt{2k} } = \frac{1}{ 2\sqrt{2} }$

→ sec A =

$\frac{1}{cosA} = \frac{3}{ 2\sqrt{2} }$

:- According to question the value of

CosA.CossecA + TanA.SecA =

$\frac{ 2\sqrt{2} }{3} \times 3 + \frac{1}{ 2\sqrt{2} } \times \frac{3}{ 2\sqrt{2} }$

$= 2\sqrt{2} + \frac{3}{8}$