Question

if ø is an acute angle. and sinø = cosø find 3tan²ø +2sin²ø+cos²ø-1​

Answer 1

Given that ∅ is acute, and the condition of sin ∅ = cos ∅ needs to be satisfied. Thus, there exists only one such value of ∅ which can possibly be the correct angle.

→ sin ∅ = cos ∅

→ sin ∅ = sin (90 - ∅) {cos x = sin (90 - x)}

→ ∅ = 90 - ∅

→ 2∅ = 90

→ ∅ = 45°

Now, this is the value of ∅ we have. We can put the trigonometric values of all ratios if this angle and find the final answer.

3 tan² ∅ + 2 sin² ∅ + cos² ∅ - 1

→ 2 tan² 45 + 2 sin² 45 + cos² 45 - 1

→ 2(1) + 2(1/√2)² + (1/√2)² - 1

→ 2 + 1 + 1/2 - 1

→ 2 - 1/2

→ 3/2 or 1.5

Note: We usually write the final answers of trigonometric functions as fractions, and not decimals, since they are ratios. So, a better answer of this question would be 3/2.

Answer 2

Answer:

0

Step-by-step explanation:

given sinø=cosø

to find: 3tan²ø+2sin²ø+cos²ø-1

=3(sin²ø/cos²ø)+2sin²ø+sin²ø

=3(1-cos²ø/cos²ø)+3sin²ø

3(cos²ø-cos²ø/cos²ø) +3sin²ø

0+3sin²ø

0 = 3sin²ø

0/3= sin²ø

0=sin²ø

√0=sinø

0=sinø

ø=0