Question

cot a - tan a = sec a. cosec a​

Answer 1

Answer:

Hi

Step-by-step explanation

We have to prove that cotA-tanA=secA.cosecA

By taking L.H.S we can prove that

(cotA-tanA)

By squaring,

(cotA-tanA)² here it looks like (a-b)²we know that

(a-b)²=a²+b²+2ab

here,a=cotA and b=tanA,let us substitute

(cotA-tanA)²=cot²A+tan²A-2(cotA)(tanA)

                     =cosec²A-1+sec²A-1-2(cotA)(tanA)[∵by using the    identities cot²A=cosec²-1 and tan²A=sec²A-1]

                     =cosec²A.sec²A+2-2(cotA)(tanA)[∵I have added both -1 and -1=+2 I have got]

                     =cosec²A.sec²A.cotA.tanA[I have cancelled both +2 and -2]

                     =cosec²A.sec²A.1[∵because cotA reciprocal is tanA and tanA reciprocal is cotA so they are side by side then we can write it as 1]

                     =cosec²A.sec²A

∴cosecA.secA or secA.cosecA=secA.cosecA

                                        ∴L.H.S=R.H.S

∴Hence proved

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