sec α+ tan α = (tan π/4+α/2)
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Answer:
Step-by-step explanation:
Let us start from Right Hand Side
tan(π4+A2)
= tan(π4)+tan(A2)1−tan(π4)tan(A2)
= 1+tan(A2)1−1⋅tan(A2)
= 1+sin(A2)cos(A2)1−sin(A2)cos(A2)
= cos(A2)+sin(A2)cos(A2)−sin(A2)
= cos(A2)+sin(A2)cos(A2)−sin(A2)×cos(A2)+sin(A2)cos(A2)+sin(A2)
= (cos(A2)+sin(A2))2cos2(A2)−sin2(A2)
= cos2(A2)+sin2(A2)+2sin(A2)cos(A2)cosA
= 1+sinAcosA
= 1cosA+sinAcosA
= secA+tanA
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