Question

if Φ1 ,Φ2,Φ3,Φ4......Φn are in ap, whose comman difference is d show that
SecΦ1•SecΦ2 + secΦ2•secΦ3+.........+secΦn-1•secΦn = tan Φn - tan Φ1/sind
​

Answer 1

Step-by-step explanation:

To prove ----->

Secφ₁ Secφ₂ + Secφ₂ Secφ₃ + ...........

+ Secφₙ _ ₁ Secφₙ = (tanφₙ - tanφ₁) / Sind

Proof----->

1) plzzz see the attachement

2) First of all we find common difference of given AP.

3) Then we take LHS

4) We know that,

Secθ = 1 / Cosθ , using it in , second step .

5) In fourth step we multiply and divide by , Sind

6) In fifth step we put value of d .

7) We know that ,

Sin ( A + B ) = SinA CosB + CosA SinB

Applying it in sixth step

8) We know that,

tanθ = Sinθ / Cosθ

applying it in 8th step , we get RHS.

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