Question

if sinA+cosecA=K, find value of cosA​

Answer 1

Step-by-step explanation:

sinA+cosecA=k

sinA+1/sina=k

sin^2-ksinA+1=0

get sinA

and after cosA=√1-sin^2A

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Answer 2

Given:- sinA + cosecA = k

To Find:- The value of cosA .

Answer :- Given that , sinA+cosecA=K .

⇒ sinA+cosecA=K .

⇒ sinA + 1/sinA = k .

⇒ sin²A + 1 / sinA = k

⇒ sin²A + 1= k sin A .

⇒ sin²A- k sinA + 1 = 0.

⇒ sinA = - b ± √b² - 4ac / 2a . [Quadratic formula]

⇒ sinA = +k ± √ k² -4×1×1/2

⇒ sinA = k ± √k² - 4/2

⇒ sinA = k + √ k² - 4 / 2 , k - √k² - 4 /2

Also , we know ;

$\boxed{\purple{\bf sin^2\phi+cos^2\phi = 1}}$

⇒ sin²A + cos²A = 1.

⇒ ( k + √(k² - 4)/2)² -1 = cos²A

⇒ cos²A = k² + k² - 4 × 2k(√k²-4)/4

⇒ cos²A = 2k² -8k(√k² - 4) /4

⇒ cosA = √ [ 2k² - 8k{√(k² - 4) }]/2

$\large\underline{\boxed{\red{\bf\green{\dag} \:\;cosA = \dfrac{\sqrt{2k^2-8k\sqrt{k^2-4}}}{2}}}}$

★Learn more from Brainly :-

1)sinA÷ cotA+cosecA - sinA÷cotA-cosecA = ????

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2)cosecA/cosecA+1= 1-sinA/sinA

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