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Question
In right angled ΔLMN, if ∠N =θ, ∠M = 90, cos θ =`24/25`, find sin θ and tan θ Similarly, find (sin2 θ) and (cos2 θ).
Solution
In right ∆LMN, ∠N = θ
cos θ = `24/25`
⇒ `"MN"/"LN" = 24/25`
Let MN = 24k and LN = 25k
Using Pythagoras theorem, we have
LN2 = LM2 + MN2
⇒ (25k)2 = LM2 + (24k)2
⇒ LM2 = 625k2 − 576k2
⇒ LM2 = 49k2
⇒ LM = `sqrt(49k^2)`
⇒ LM = 7k
Now,
sin θ = `["LM"]/["LN"] = [7k]/[25k] = 7/25`
tan θ = `["LM"]/["NM"] = [7k]/[24k] = 7/24`
Also,
sin2 θ = `( 7/25)^2 = 49/625`
cos2 θ = `(24/25)^2 = 576/625`
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