1. If sec θ + tan θ = 2 + √5, then the value of sin θ + cos θ is :
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By: anil on 05 May 2019 01.57 am
given sec θ + tan θ = 2 + √5-------(1) we know that, $$sec^{2}θ-tan^{2}θ=1$$ $$(sec θ + tan θ).(sec θ - tan θ)=1$$
(2 + √5).(sec θ - tan θ)=1 (sec θ - tan θ)=√5-2 ------(2)
on solving (1)&(2) secθ=√5 $$Rightarrow$$ cosθ=1/√5 tan θ=2 $$Rightarrow$$ sin θ/cosθ=2 $$Rightarrow$$ sinθ=2.cosθ $$Rightarrow$$ sinθ =2/√5 $$Rightarrow$$ sin θ + cos θ = 1/√5 + 2/√5
$$Rightarrow$$ sin θ + cos θ = 3/√5
so the answer is option A.
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(2 + √5).(sec θ - tan θ)=1 (sec θ - tan θ)=√5-2 ------(2)
on solving (1)&(2) secθ=√5 $$Rightarrow$$ cosθ=1/√5 tan θ=2 $$Rightarrow$$ sin θ/cosθ=2 $$Rightarrow$$ sinθ=2.cosθ $$Rightarrow$$ sinθ =2/√5 $$Rightarrow$$ sin θ + cos θ = 1/√5 + 2/√5
$$Rightarrow$$ sin θ + cos θ = 3/√5
so the answer is option A.