Question

if tan A = 3/4 then find the value of cos^2A -sin^2A

Answer 1

tanA = 3/4

we know
tanA = opposite side/adjacent side

so opposite side = 3

adjacent side = 4

then tangent becomes 5
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cos²A - sin²A

= (4/5)²-(3/5)²

= 16/25 - 9/25

= 16-9/25

= 7/25
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Answer 2

Answer: The answer is 7/25.

Step-by-step explanation:

Here, tan A = $\frac{3}{4}$

Since, sec² A = 1 + tan² A

$\implies sec^2 A = 1 + ( \frac{3}{4})^2$

$\implies sec^2 A = 1 + \frac{9}{16} = \frac{16+9}{16}=\frac{25}{16}$

$\implies sec A = \frac{5}{4}$

Now, cos A = 1/sec A

$\implies cos A = \frac{4}{5}\implies cos^2 A =\frac{16}{25}$

And, sin² A = 1 - cos² A,

$\implies sin^2 A = 1 - (\frac{4}{5})^2= 1 -\frac{16}{25}=\frac{25-16}{25}=\frac{9}{25}$

Hence,

$cos^2A -sin^2A=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}$