sin2 20° + sin2 70°/2 (cos2 69° + cos2 21°) =sec60/k
then find the value of k.
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Answer:
k = 4
Step-by-step explanation:
L.H.S:
[sin²20° + sin²70°] / 2(cos²69° + cos²21°)
//sinθ = cos(90-θ); cosθ = sin(90 - θ)
sin70° = cos(90-70) = cos20°
cos69° = sin(90-69) = sin21°
=> [sin²20° + sin²70°] / 2(cos²69° + cos²21°)
=> [sin²20° + cos²20°] / 2 (sin²21° + cos²21°)
=> 1/2
R.H.S = L.H.S
Sec60/k = 1/2
2/k = 1/2
k = 4.
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