Question

If tan C=3/4 then find the value of cos²C-sin²C

Answer 1

Step-by-step explanation:

Tan C = 3/4 (given)

From Pythogoras Theorem

$ac {}^{2} = ab {}^{2} + bc {}^{2}$

$ac {}^{2} = 3 {}^{2} + 4 {}^{2}$

$ac {}^{2} = 9 + 16$

$ac {}^{2} = 25$

$ac = \sqrt{25}$

$ac = 5$

cos C = 4/5

sin C = 3/5

As per the question

$cos {}^{2} c - sin {}^{2} c \: = \frac{16}{25} - \frac{9}{25}$

$= \frac{7}{25}$