If sec theta - tan theta = root2.tan theta, then show that sec theta + tan theta = root2.sec theta (root2 is alone...not multiplied with tan theta or sec theta)
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Sec theta - tan theta =√2 tan theta (given)
Sec theta = √2 tan theta + tan theta
Sec theta = (√2+1)tan theta
Sec theta = tan theta (√2+1) × (√2-1)/(√2-1) Multiplying numerator and denominator with (√2-1)
Sec theta = tan theta [(√2)2 – (1)2]/ (√2-1)
Sec theta (√2-1)= tan theta
√2 sec theta - sec theta= tan theta
Sec theta + tan theta= √2 sec theta
Answered by
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Sec theta - tan theta =√2 tan theta
Sec theta=√2 tan theta + tan theta
Sec theta =(√2+1)tan theta
Now rationalise
Sec theta =tan theta (√2+1)×(√2-1)/(√2-1)
Sec theta (√2-1)= tan theta
√2 sec theta - sec theta= tan theta
Sec theta + tan theta= √2 sec theta
proved....
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