solve the following equation when theta is greater than zero and less than 90 if 3 tan theta + cot theta is equal to 5 cosec theta
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Answered by
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3tanA+cotA=5cosecA {A=theta}
L.H.S
3tanA+cotA
=>3×sinA/cosA+cosA/sinA
=>(3sinA)/cosA+cosA/sinA
TAKING COSASINA AS LCM
=>(3sinA×sinA+cosA×cosA)cosAsinA
=>(3sin^2A+cos^2A)cosAsinA {sin^2A+cos^A}
=>3/cosAsinA
FIGURE IT OUT YOURSELF
Answered by
1
Step-by-step explanation:
lets say theta as •
GIVEN : 3TAN• + COT• = 5COSEC•
step1: convert all functions in sine and cosine
so ,. 3sin•/cos• + cos•/sin• = 5/sin• on solving
[3(sin•)^2 + (cos•)^2]= 5cos•
put (sin•)^2 as 1-(cos•)^2
and on solving this we get a quadratic equation as
2(cos•)^2 + 5cos• - 3 = 0
this gives cos• values as -3 and 1/2.
since cos • can't be less than -1 ...
cos• = 1/2 and in the given range • = π/3
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