if 2 sec theta+3 tan theta=5 then (2 tan theta+3sec theta)^(2)=
Please answer my question quickly please
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if 2 sec theta+3 tan theta=5 then (2 tan theta+3sec theta)^(2)=
Please answer my question quickly please
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Given : (2secθ + 3 tanθ) = 5
To find : (2tanθ + 3 secθ)²
Solution:
(2secθ + 3 tanθ) = 5
Squaring both sides
=> 4sec²θ + 9 tan²θ + 12secθtanθ = 25
=> 4(1 + tan²θ) + 9 (sec²θ - 1) + 12secθtanθ = 25
=> 4 + 4 tan²θ + 9sec²θ - 9 + 12secθtanθ = 25
=> 4 tan²θ + 9sec²θ + 12secθtanθ = 30
=> (2tanθ + 3 secθ)² = 30
Hence (2tanθ + 3 secθ)² = 30
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