Question

Prove that cos a minus sin a ×sec A minus Cos A × tan A + cot a = 1

Answer 1

Step-by-step explanation:

LHS =(tanA+cotA)(cosecA-SinA)(secA-CosA)

tanA+cotA=(SinA/CosA)+(CosA/SinA)

= (sin²Α+cos²Α)/cosAsinA

= 1/cosAsinA

CosecA-SinA=(1/SinA)-SinA

= (1-sin²Α)/SinA= cos²Α/sinA

SecA-cosA=(1/cosA)-cosA=(1-cos²Α)/cos A

=sin²Α/cosA

(tanA+cotA)(cosecA-SinA)(secA-cosA)

=(1/sinAcosA)(cos²Α/SinA)(sin²Α/CosA)

=1=RHS

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