Question

if sinA-cosA=2 then find the value of sec⁴A+cos⁴A​

Answer 1

❏ Used Formulas

(1) X²+Y²=(X+Y)²-2XY

(2) X²+Y²=(X-Y)²+2XY

(3) sin²X+cos²X=1

❏ Solution

Q) if sinA-cosA=2 ,then find the value of

sin⁴A+cos⁴A=?

Ans)

Now, sinA-cosA=2

[squaring on both sides]

➾(sinA-cosA)²=2²

➾ sin²A+cos²A-2.sinA.cosA=4

➾ 1-2.sinA.cosA=4

➾ -2.sinA.cosA=4 -1

➾ sinA.cosA= $\sf\frac{-3}{2}$

Now,,,

sin⁴A+cos⁴A

➾(sin²A)²+(cos²A)²

➾(sin²A+cos²A)²-2 sin²A cos²A

➾(1)²-2(sinA cosA)²

➾ 1+($\sf\frac{-3}{2}$)²

➾ 1+ $\sf\frac{9}{4}$

➾ $\sf\frac{4+9}{4}$

➾ $\sf\frac{13}{4}$

➾ sin⁴A+cos⁴A= $\sf\frac{13}{4}$

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