Question

Find the value of cos square 55+cos square 35​

Answer 1

Answer

1

$\sf\rule{200}2$

Explanation

To find the value of

cos²(55°) + cos²(35°)

We know that,

sin(∅) = cos(90° - ∅), and

cos(∅) = sin(90° - ∅)

Hence, cos(35°) = sin(90° - 35°)

→ cos(35°) = sin(55°)

Hence,

cos²(55°) + cos²(35°) becomes

cos²(55°) + sin²(55°)

Now, we know that

sin²∅ + cos²∅ = 1

Hence,

cos²(55°) + sin²(55°) = 1

→ cos²(55°) + cos²(35°) = 1

$\rule{200}2$

Additional Information

Proof of cos²∅ + sin²∅ = 1

We know that cos∅ = B/H and sin∅ = P/H

So, cos²∅ + sin²∅ = (B/H)² + (P/H)²

→ B²/H² + P²/H²

→ (P² + B²)/H²

→ H²/H² (By Pythagoras theorem, P² + B² = H²)

→ 1

Hence, cos²∅ + sin²∅ = 1

Answer 2

Answer:

2 sin^2(35)

Step-by-step explanation:

cos55=cos(90-35)= sin35

cos^2(55)= sin^2(35)

cos35= - sin35

cos^2(35)= sin^2(35)

cos^2(55)+cos^2(35)= sin^2(35)+ sin^2(35)

=2sin^2(35)