Question

from the figure the value of 25 (sin² theta + 2cos² theta - tan theta) is
(a) 2/3
(b) -2/3
(c) 3/2
(d) -3/2​

Answer 1

Answer:

a) 2/3

Step-by-step explanation:

sinØ = Perpendicular/Hypotenuse

= PQ/PQ

= 8/10

cosØ = Base/Hypotenuse

= QR/PR

= 6/10

tanØ = Perpendicular/Base

= PQ/QR

= 8/6

Now,

→ 25 (sin²Ø + 2cos²Ø - tanØ)

Substitute the values,

→ 25 [(8/10)² + 2(6/10)² - 8/6)

→ 25 (64/100 + 2*36/100 - 8/6)

→ 25 (64/100 + 72/100 - 8/6)

→ 25 (192 + 216 - 400)/300

→ 25(8/300)

→ 8/12

→ 2/3

Therefore the value of 25 (sin²Ø + 2cos²Ø - tanØ) is 2/3.

Answer 2

$\begin{gathered}\huge\blue{\mid{\fbox{\tt{SOLUTION}}\mid}} \\ \end{gathered}$

Correct answer - ( a ) $\frac{2}{3}$