Question

Evaluate sin² $\frac{2\pi}{3}$ + cos² $\frac{5\pi}{6}$ - tan² $\frac{3\pi}{4}$.

Answer 1

sin²2π/3 + cos²5π/6 - tan²3π/4

we know,

sin2π/3 = sin(π - π/3) = sinπ/3 = √3/2

so, sin²2π/3 = (√3/2)² = 3/4

cos5π/6 = cos(π - π/6) = -cosπ/6 = -√3/2

so, cos²5π/6 = (-√3/2)² = 3/4

tan3π/4 = tan(π - π/4) = -tanπ/4 = -1

so, tan²3π/4 = (-1)² = 1


now, sin²2π/3 + cos²5π/6 - tan²3π/4

= 3/4 + 3/4 + 1

= 3/2 + 1

= 5/2

Answer 2

Answer:1/2

Step-by-step explanation:

sin²2π/3 + cos²5π/6 - tan²3π/4

we know,

sin2π/3 = sin(π - π/3) = sinπ/3 = √3/2

so, sin²2π/3 = (√3/2)² = 3/4

cos5π/6 = cos(π - π/6) = -cosπ/6 = -√3/2

so, cos²5π/6 = (-√3/2)² = 3/4

tan3π/4 = tan(π - π/4) = -tanπ/4 = -1

so, tan²3π/4 = (-1)² = 1

now, sin²2π/3 + cos²5π/6 - tan²3π/4

3/4+3/4-1

= 1/2