sin Q +secQ - cosecQ =tanQ +cotQ
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Step-by-step explanation:
(sinΘ+cosΘ)(tanΘ+cotΘ)
as we know tan Θ = sinΘ/cosΘ and cot Θ = cos Θ/sinΘ lets apply that
(sinΘ+cosΘ)(sinΘ/cosΘ + cosΘ/sinΘ)
(sinΘ+cosΘ)(sin^2Θ + cos ^2Θ / sin Θ x cos Θ)
(sinΘ+cosΘ)( 1 / sin Θ x cos Θ) ( because sin^2Θ + cos^2Θ = 1)
(sinΘ+cosΘ)/( sin Θ x cos Θ)
sinΘ/ sin Θ x cos Θ + cosΘ/ sin Θ x cos Θ ( distribute property)
1/cosΘ + 1/sinΘ
secΘ+cscΘ = RHS
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sinΘ+cosΘ)(tanΘ+cotΘ)
as we know tan Θ = sinΘ/cosΘ and cot Θ = cos Θ/sinΘ lets apply that
(sinΘ+cosΘ)(sinΘ/cosΘ + cosΘ/sinΘ)
(sinΘ+cosΘ)(sin^2Θ + cos ^2Θ / sin Θ x cos Θ)
(sinΘ+cosΘ)( 1 / sin Θ x cos Θ) ( because sin^2Θ + cos^2Θ = 1)
(sinΘ+cosΘ)/( sin Θ x cos Θ)
sinΘ/ sin Θ x cos Θ + cosΘ/ sin Θ x cos Θ ( distribute property)
1/cosΘ + 1/sinΘ
secΘ+cscΘ = RHS
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