Question

Prove: (1+ tan square theta)(1+ sin theta)(1 - sin theta) = 1
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Answer 1

To prove:

(1+tan²A)(1+sinA)(1-sinA)=1

★Formulas to be used,

•sec²A-tan²A=1→1+tan²A=sec²A

•sin²A+cos²A=1→1-sin²A=cos²A

•cosA=1/secA→cos²A=1/sec²A

Now,

LHS:

(1+tan²A)(1+sinA)(1-sinA)

=(1+tan²A)(1-sin²A)

=sec²Acos²A

=1

=RHS

Hence,proved