Question

plz help me all of you plz plz ​

Answer 1

Answer:

see the above attachment ✔✔

Answer 2

Answer:

The required answer is √3

Step-by-step explanation:

First

Sin²θ + 2Cos²θ + 3Sin²θ + 4Cos²θ + - - - - - - 40 terms

= ( Sin²θ + 3Sin²θ + - - ------ - 20terms) + ( 2Cos²θ + 4Cos²θ + - - - ------ - 20 terms)

= Sin²θ ( 1+3+--------- 20terms) + 2Cos²θ ( 1+2+ - - - - - - 20terms)

= Sin²θ [ 20/2 ( 2 + 19× 2)] + 2Cos²θ [ 20/2 ( 2 + 19× 1)]

= 400 Sin²θ + 420 Cos²θ

So

400 Sin²θ + 420 Cos²θ = 405

400 Sin²θ + 420 Cos²θ = 405 ( Sin²θ + Cos²θ)

5 Sin²θ = 15 Cos²θ

tan²θ = 3

tanθ = √3

So the required answer is √3