Question

solve this ques fast pls
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SecA +TanA=x
find the value of SinA

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Answer 1

secA+tanA=x.........(1.) and we know that sec2A-tan2A=1 ON DIVIDING with  given result with eqn.1secX-tanX=1/x(2.)

now solve eqn(1.)and(2.) by simple linear  equation method to obtain required ratios. 

Answer 2

Answer:

(x² + 1)/(x² - 1)

Step-by-step explanation:

Given, secA + tanA = x.   ------------- (1)

We know that : (secA + tanA)(secA - tanA) = 1

⇒ (x)(secA - tanA) = 1

⇒ secA - tanA = (1/x)    ----------------- (2)

On subtracting, we get

⇒ 2tanA = x - (1/x)

⇒ 2 tanA = (x² - 1)/x

⇒ tanA = (x² - 1)/2x

∴ cotA = 1/tanA

           = (2x)/x² - 1

∴ cosec²A = 1 + cot²A

                 = 1 + [(2x/x²- 1)]²

                 = (x⁴ - 2x² + 1 + 4x²)/(x² - 1)²

                 = (x⁴ + 2x² + 1)/(x² - 1)²

                 = (x² + 1)²/(x² - 1)²

                = (x² + 1)/(x² - 1).

∴ sinA = 1/cosecA

           = (x² + 1)/(x² - 1).

Hope it helps!