Question

If 3cotA = 4, then the value of cos square A - sin square A is
Please answer in a little bit detail ​

Answer 1

Step-by-step explanation:

3cotA=4

so cotA = 4/3

tanA= 3/4

A= 37°

Now

cos^2(A) - sin^2(A) = cos^2(37°) - sin^2(37°)= 0.275

Answer 2

Answer:

cos²A - sin²A =$\frac{7}{25}$

Step-by-step explanation:

Given,

3cotA = 4

To find,

cos²A - sin²A

Recall the formula

cot A = $\frac{adjacent \ side }{opposite \ side}$

sin A = $\frac{opposite \ side }{hypotenuse}$

cos A = $\frac{adjacent \ side }{hypotenuse}$

Solution

Since 3 cot A = 4, cot A = $\frac{4}{3}$

cot A = $\frac{adjacent \ side }{opposite \ side}$  = $\frac{4}{3}$

adjacent side = 4 and opposite side = 3

∴hypotenuse = $\sqrt{4^2+3^2}$ = 5

cos A = $\frac{adjacent \ side }{hypotenuse}$ = $\frac{4}{5}$

sin A = $\frac{opposite \ side }{hypotenuse}$ = $\frac{3}{5}$

cos²A - sin²A = ( $\frac{4}{5}$)² - ( $\frac{3}{5}$)²

= $\frac{16}{25}$ -  $\frac{9}{25}$

=$\frac{7}{25}$

∴ cos²A - sin²A =$\frac{7}{25}$

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