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# 5. Which of the following are true?Plz give steps.

Abhishek Jain
19 Points
3 years ago
option A, B and D are true.
that is because of the reasons-
1. sin 37= cos(90-37)=cos 53
2. cos 37=sin(90-37)=sin 53
3. tan (a)=1/(tan(90-a) OR tan a * tan (90-a) = 1
Vikas TU
14149 Points
3 years ago
Dear Student,
In ques 5, lets consider a right angled triangle ABC with angle A=53,B=90,C=37.
And as it is a standard triangle, the sides AB=3,BC=4 and CA=5,
so sin 37=3/5,
cos 37=4/5,
tan 37=3/4.
And sin 53=4/5,
cos 53=3/5 and
tan 53=4/3.
Now optionA: LHS= sin 37+cos 37=3/5 + 4/5 =1 and RHS=sin 53+cos53=4/5+3/5=1 so it is true.
Option B: LHS= sin 37-cos 37=3/5 -4/5 =-1 and RHS= cos53-sin 53=3/5-4/5=-1 so it is true
Option C:LHS=tan 37+1=3/4+1=7/4 RHS=tan 53-1=4/3-1=1/3  so it is not true
Option D:LHS: tan 37 * tan 53=1 =RHS, so it is true
Therefore, option A,B and D are true.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
Suresh
13 Points
3 years ago
Hey for the 6th question is the option three (3) is it right guys.ok guys say fast A square + A square + 2A square cos theta = 2A square cos theta
Soumendu Majumdar
159 Points
3 years ago
Options A, B & D are correct! as sin 53=cos37 & cos53=sin37 using sin A=cos(90-A)
AND tan A = cot(90-A)
Using the above you will find that the options mentioned above are correct

Hope it helps..