Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If 
cos α + 
sin α = 1, 
cos β + 
sin β = 1 and
+ 
= 0, then –
A
tan α tan β = 
B
x 2 + y 2 = a 2 + b 2
C
tan α tan β = 
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b)
cos α + 
sin α = 1 ……(1)
cos β + 
sin β = ……(2)
+ 
=0 .…...(3)
From (1) and (2). we get
x = a 
and y = b 
Now, x 2 + y 2
= 
= 
= 
[From (3)]
= a 2 + b 2 + 
= a 2 + b 2 + 
= 2 + b 2 +
a 2 + b 2 +
a 2 +b 2 + 
[from (3)]
= a 2 + b 2 + 0 = a 2 + b 2 Thus, x
2 + y 2 = a 2 + b 2 therefore choice is correct
Now, x 2 + y 2 = a 2 + b 2 ⇒ x
2 – a 2 = – (y 2 – b 2 )
⇒ 
= – 1
⇒ 
= – 
= tan α tan β
[from (3)]
∴ choice is also correct
Thus, and both are correct.
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