Question

Solve the trigonometric function tan∅ × sin∅ × cos∅ + cos2∅

Answer 1

Answer:

cos²Θ

Step-by-step explanation:

simplify the expression using the identities

tanΘ = $\frac{sin0}{cos0}$

cos2Θ = 1 - 2sin²Θ

cos²Θ = 1 - sin²Θ

then

tanΘ × sinΘ × cosΘ + cos2Θ

= $\frac{sin0}{cos0}$ × sinΘ × cosΘ + 1 - 2sin²Θ ( cancel cosΘ on numerator/ denominator )

= sinΘ × sinΘ + 1 - 2sin²Θ

= sin²Θ + 1 - 2sin²Θ

= 1 - sin²Θ

= cos²Θ

Answer 2

Answer:

$\cos^2(\theta)$

Step-by-step explanation:

Trig identities used:

$\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)$

$\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}$

Therefore,

$\tan(\theta)\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)$

$=\dfrac{\sin(\theta)}{\cos(\theta)}\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)$

$=\sin^2(\theta) +\cos(2\theta)$

$=\sin^2(\theta) +\cos^2(\theta)-\sin^2(\theta)$

$=\cos^2(\theta)$