Prove that tan a + sec a-1÷ tan a - sec a + 1 = 1 + sin a ÷ cos a
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Step-by-step explanation:
tanA+secA-1/tanA-secA+1× tanA-secA/tanA-secA
={(tanA+secA)-1}(tanA-secA) /(tanA-secA+1)(tanA-secA)
=tan²A-sec²A-tanA+secA /(tanA-secA+1)(tanA-secA)
=-1-tanA+secA/(tanA-secA+1)(tanA-secA)
=-(tanA-secA+1)/ (tanA-secA+1)(tanA-secA)
=-1/tanA-secA
=1/secA-tanA×secA+tanA/secA+tanA
=secA+tanA/sec²A-tan²A
=secA+tanA
=(1/cosA)+(sinA/cosA)
=1+sinA/cosA
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