AP EAMCET202120 Aug 2021Morning ShiftMathematicsMatricesActual
If 1 - tan θ tan θ 1 1 tan θ - tan θ 1 - 1 = a - b b a , then
Options
- Aa = 1 , b = 1
- Ba = cos 2 θ , b = sin 2 θ
- Ca = sin 2 θ , b = cos 2 θ
- DNone of these
Correct answer
B. a = cos 2 θ , b = sin 2 θ
Step-by-step solution
Assume, A = 1 tan θ - tan θ 1 A = 1 + tan 2 θ and Adj A = 1 - tan θ tan θ 1 We know, A - 1 = Adj A A Given, 1 - tan θ tan θ 1 1 tan θ - tan θ 1 - 1 = a - b b a ⇒ 1 - tan θ tan θ 1 1 1 + tan 2 θ 1 - tan θ tan θ 1 = a - b b a ⇒ 1 1 + tan 2 θ 1 - tan 2 θ - 2 tan θ 2 tan θ 1 - tan 2 θ = a - b b a ⇒ 1 - tan 2 θ 1 + tan 2 θ - 2 tan θ 1 + tan 2 θ 2 tan θ 1 + tan 2 θ 1 - tan 2 θ