Question

If 4 tan theta = 3 then (cos² theta - sin² theta)=?​

Answer 1

Answer:

7/25

Step-by-step explanation:

here tan theta = 3/4 therefore sin theta = 3/5

now cos^2 theta - sin^2 theta = 1-2sin^2 theta

=1-2(3/5)^2

=1- 18/25

=7/25 ans .

Answer 2

Solution :-

$\sf \tan \theta = \dfrac{3}{4}$

We know :-

$\bf \star \: { \tan}^{2} \theta + 1 = { \sec}^{2} \theta$

$\bf \star \: \cos \theta = \dfrac{1}{ \sec \theta}$

$\bf \star \: \sin \theta = \tan \theta \times \cos \theta$

$: \implies \sf \sec \theta = \sqrt{ { \left( \dfrac{3}{4} \right)}^{2} + 1}$

$: \implies \sf \sec \theta = \sqrt{ \dfrac{25} {16}}$

$: \implies \bf \sec \theta = \dfrac{5}{4}$

$: \implies \bf \cos \theta = \dfrac{4}{5}$

$: \implies \bf \sin \theta = \dfrac{3}{5}$

$: \implies \sf \cos ^2 \theta- \sin ^2 \theta = \dfrac{4^2-3^2}{5^2}$

$: \implies \sf \cos ^2 \theta- \sin ^2 \theta = \dfrac{16-9}{25}$

$\underline{: \implies \bf \cos ^2 \theta- \sin ^2 \theta = \dfrac{7}{25}}$