Doubt in trigonometry

Any innovative idea for 82 question.

Answer is option A

Help @Sneha_2021 @Shwetanshu_2018 @Hari_Shankar sir @Abhishek_2020_5

Getting 1st option by putting every thing =π/4

see the jension inequality will help with little more approximation
Sin(\alpha+....)\geqslant Sin(\alpha)+....

not exact jension but by symmatri i thought of this concept

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Do you need some alternate method or just quick answer ? For quick answer you can put a value and check

I thought of this but how can we be sure that for other value the exception will not be there.

Thanks a lot @Tanmay_1 Sir

Most welcome

See , if it’s single correct then for sure it should be A and then you simply can move forward to other questions during exam but if it is multiple correct type , then this trick won’t work .
Putting and checking isn’t a method to solve the question , it is just that during exam , it doesn’t matter that you solved the question and got the answer or you simply applied some ‘jugaad’ . So obviously you should not do such things while practising at home , but during exam , for sure such things should be used .

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