if 1-sin2a/cos2a=tan theta then the value of theta is
Answers
Given : (1 - sin2a)/cos2a = tanθ
To Find : Value of θ
Solution:
(1 - sin2a)/cos2a = tanθ
1 = sin²a + cos²a
cos2a = cos²a - sin²a
sin2a = 2sinacosa
=> ( sin²a + cos²a - 2sinacosa)/( cos²a - sin²a) = tanθ
=> ( ±(cosa - sina))²/(cos + sina)(cosa - sina) = tanθ
=> ( ±(cosa - sina)) /(cos + sina) = tanθ
Dividing numerator & denominator by cosa in LHS
=> ± ( 1 - tana)/(1 + tana) = tanθ
1 = tan(π/4)
=> ±( tan(π/4) - tana)/(1 + tan(π/4).tana) = tanθ
=> ±tan((π/4) - a) = tanθ
=> θ = (π/4) - a , a - (π/4)
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Answer:
45
Step-by-step explanation:
1-sin2=cos
tan =1
tan 45 =1