Question

Plz help me out of this !

1)

Assertion:- cos1<cos2
Reason :- In (0, π) ,cosx is decreasing function

Options :-
Both are correct
Both are incorrect
A is correct B is incorrect
A is incorrect B is correct


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2)
Assertion:- cos20° - sin20° >0
Reason :- If θ belongs to R , cosθ-sinθ> 0

Options :-
Both are correct
Both are incorrect
A is correct B is incorrect
A is incorrect B is correct





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Answer 1

Answer:

For question 1

Assertion is incorrect reason is correct. hence option fourth

as we know that cos x is decreasing function in x belongs (0,π) So cos1 will be greater than cos2

For question 2

Assertion is correct but reason is incorrect as

Cos function is decreasing function from (0,π) and sin function is increasing function from (0,π) hence the value of Cos x will decrease from 0 to π and value of sin x will increase from 0 to π

but they both will give same value at 45° which means from 0 to 45° cos function will be greater than sin function

hence value of Cos 20° will be greater than sin20° but not for every value of theta because you can see in graph sometimes sin function gives greater value than cos function.

so the value of cos20°-sin20° will be positive

Go through attachment for better understanding

Answer

1. A is incorrect R is correct
2. A is correct R is incorrect

Answer 2

Question:-

Assertion:- cos1 < cos2

Reason :- In (0, π) ,cos x is decreasing function

Options :-

(a) Both are correct

(b) Both are incorrect

(c) A is correct R is incorrect

(d) A is incorrect R is correct

Answer:-

It is known to us that cos 1 will be greater than cos 2 because cos x is decreasing function in x in (0, π)

∴ (d) Assertion is false but reasoning is true.

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Question:-

Assertion:- cos20° - sin20° >0

Reason :- If θ belongs to R , cosθ-sinθ> 0

Options :-

(a) Both are correct

(b) Both are incorrect

(c) A is correct R is incorrect

(d) A is incorrect R is correct

Answer:-

As we know from above answer that value of Cos x will decrease (0 -π) and we know value of sin x will increase (0 - π).

There is only 1 condition they both will give same value that is Ф should be 45° i.e. from 0 to 45° cos function will be greater than sin function  

∴ (c) Assertion is true but reason is false.

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