Question

TanA+cotA=1/sinA cosA

Answer 1

Answer:

LHS

tanA + cotA

=sinA/cosA + cosA/sinA

On cross multiplication,

=sin^2A + cos^2A/sinAcosA

=1/sinAcosA. (since sin^2A + cos^2A=1)

=RHS

hence proved

Answer 2

Answer:

TanA+cotA=1/sinA cosA; Hence LHS= RHS proved.

Step-by-step explanation:

• TanA+cotA=1/sinA cosA
  According to trigonometric formula,

• tanA = sinA/cosA
• CotA = cosA/sinA
• Sin²A + cos²A = 1
  Now breaking this sum into sine cosine-
  TanA+cotA=1/sinA cosA
  LHS = sinA/cosA+cosA/sinA
         =[(sinA×sinA)+(cosA×cosA)/sinA cosA]
          = (sin²A+cos²A/sinAcosA)
          = 1/sinAcosA [• Sin²A + cos²A = 1]
  LHS = RHS
  Hence proved that LHS = RHS I.e TanA+cotA=1/sinA cosA
  
  Other formulas of trigonometry

• Sec²A+tan²A = 1
• Cosec²A+cot²A = 1
• SinA.cosA = 1
• SinA = 1/cosecA
• CosA = 1/secA
• TanA = 1/cotA, OR sinA/cosA
  
  
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