Question

prove that sec
$\alpha$
+ tan
$\alpha$
= tan(π/4+
$\alpha$
/2
​

Answer 1

Answer:

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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