If sin 0 + cos 0 = V2 , prove that tan 0 + cot 0 = 2
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Step-by-step explanation:
Given:-
Given sin 0 + cos 0 = √2
To Prove:-
Tan 0 + Cot 0=2
Solution:-
Given that Sin 0+ Cos 0=√2
On squaring both sides then
=>(Sin 0+Cos 0)²=(√2)²
=>Sin² 0+ Cos² 0+2 Sin 0 Cos 0=2
=>1+2 Sin 0 Cos 0=2
=>2 Sin 0 Cos 0=2-1
=>2 Sin 0 Cos 0=1
=>Sin 0 Cos 0=1/2 ------(1)
LHS:-
Tan 0+ Cot 0
=>(Sin 0/Cos 0)+(Cos 0/Sin 0)
=>(Sin² 0+Cos²0)/Sin 0 Cos 0
=>1/Sin 0 Cos 0
=>1/(1/2)
=>1×(2/1)
=>2
=>RHS
LHS=RHS
Answer:-
Tan 0 + Cos 0=2
Hence, Proved
Used formulae:-
- Tan A= Sin A/Cos A
- Cot A=Cos A/Sin A
- Sin² A+Cos² A=1
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