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# Prove:(Sin A/Sec A+tan A-1)+(Cos A/Cosec A+Cot A-1)=1

Grade:10

## 3 Answers

Arun
25763 Points
3 years ago
Dear student

(SinA * cosA )/(1 + sinA - cosA)  + (cosA* sinA)/(1 + cosA - sinA)
= (SinA * cosA) [1/(1 + sinA - cosA)  +  1/(1 + cosA -sinA)]

On taking LCM and then solving

= 2 sinA cosA/ 2 sinA cosA
= 1 = RHS

Hence proved

Regards
Arun (askIITians forum expert)
Mohammad Aamir
30 Points
3 years ago
(SinA/SecA +TanA -1) + ( cosA/cosecA + cotA - 1) = 1Solution(SinA.CosA + tanA- 1) + (cosA.Sin A +CotA - 1)Put A=45(1/root 2×1/root2 +1-1) + (1/root2×1/root2 +1-1)(1/2+1-1)+(1/2+1-1)1/2+1/21 proved
gg hh
13 Points
2 years ago
(SinA/SecA +TanA -1) + ( cosA/cosecA + cotA - 1) = 1Solution(SinA.CosA + tanA- 1) + (cosA.Sin A +CotA - 1)Put A=45(1/root 2×1/root2 +1-1) + (1/root2×1/root2 +1-1)(1/2+1-1)+(1/2+1-1)1/2+1/21

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