Question

sin2^20+sin2^70+cos48cosec42+sin40sec50

Answer 1

sin²20+cos²20+cos 48sec 48+sin 40/cos50

(since cos²20=sin²70; cosec 42=sec 48;

sec 50=1/cos 50)

=1+1+sin40/sin40 (since sin²20+cos²20=1;sin40=cos 50)

=1+1+1=3

Step-by-step explanation:

hopefully it helps

Answer 2

Question :

Find the Value of sin²20° + sin²70° + cos48°cosec42° + sin40°sec50°

AnswEr :

First of all let's know some facts related to complementary angles of trigonometry.

• sin θ = cos (90° - θ)
• cos θ = sin (90° - θ)
• cosec θ = sec (90° - θ)
• sec θ = cosec (90° - θ)
• tan θ = cot (90° - θ)
• cot θ = tan (90° - θ)

• Let's Head to the Question Now :

⇒ sin²20° + sin²70° + cos48°cosec42° + sin40°sec50°

⇒ sin²20° + sin²(90° - 20°) + cos48°cosec(90° - 48°) + sin40°sec(90° - 40°)

• Using the Above Values

⇒ sin²20° + cos²20° + cos48°sec48° + sin40°cosec40°

• sec θ = 1 / cos θ
• cosec θ = 1 / sin θ
• (sin² θ + cos² θ) = 1

⇒ (sin²20° + cos²20°) + cos48°×1/cos48° + sin40°×1/sin40°

⇒ 1 + 1 + 1

⇒ 3

჻ Therefore, Value will be Equal to 3.