Question

Question 4 State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B (ii) The value of sinθ increases as θ increases (iii) The value of cos θ increases as θ increases (iv) sinθ = cos θ for all values of θ (v) cot A is not defined for A = 0°

Class 10 - Math - Introduction to Trigonometry Page 187

Answer 1

hope u get the answer only for 1 quad

Answer 2

i) FALSE

Let A= 60° & B= 30°
Then , sin(A+B) =sin (60°+30°)= sin 90°= 1.

sin(A+B)=1

sinA+ sinB = sin60° sin30°
= √3/2 + 1/2 = (√3+1)/2

sinA+ sinB =(√3+1)/2

so , sin(A+B) ≠ sin A + sin B

ii) TRUE
Observe the table given below
sin 0°= 0
sin 30°= 1/2
sin 45°= 1/√2
sin 60°= √3/2
sin 90°= 1

From this table it is clear that value of sin θ increases at θ increases.

iii) FALSE
 
Observe the table given below
cos 0°= 1
cos 30°= √3/2
cos45°= 1/√2
cos 60°= √1/2
cos 90°= 0


From this table it is clear that value of cos θ decreases at θ increases.

iv)
FALSE
Because it is only true for θ= 45°

sin45° = 1/√2= cos45°

v)
TRUE

Because if A= 0°, then cotA= 1/tanA
cotA= 1/tan0°= 1/0 = ∞ (not defined)

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Hope this will help you....