Question

please help fast!! plz plz!!

Answer 1

Solution:-
Here I am expressing theta as ©.
LHS :-
sin © - cos © + 1 / sin © + sin© - 1
= {(sin © / cos ©) - (cos © / cos ©) + (1/ cos ©)} ÷ {(sin © / cos ©) + (cos © / cos ©) - (1/cos ©)}. [dividing cos © in the equation ]
= (tan © - 1 + sec ©) / (tan © + 1 - sec ©)
={(tan © + sec ©) - 1} / {(tan © - sec ©) + 1}
=[{(tan © + sec ©) - 1}(tan © + sec ©)]÷[{(tan © - sec ©) + 1}(tan © - sec ©)
= {(tan ²© + sec ² ©) - ( tan © + sec ©)} ÷ {(tan © - sec ©) + 1}(tan © - sec ©)
= (-1 - tan © + sec ©) ÷ {(tan © - sec © + 1)(tan © - sec ©)
= - 1 / tan © - sec ©
= 1 / sec © - tan © [Hence Proved]



Please Kindly prefer Class 10 NCERT Mathematics chapter 8 Page 192 Example 15