Step-by-step explanation:
To prove :
( 1 - sin x ) ( 1 + sin x ) = sec² x
LHS : -
( 1 - sin x ) ( 1 + sin x )
Formula / Identity : -
( a - b ) ( a + b ) = a² - b²
Here,
a = 1
b = sin x
( 1 - sin x ) ( 1 + sin x )
= 1 - sin² x
Identify : -
sin² θ + cos² θ = 1
cos² θ = 1 - sin² θ
Similarly,
1 - sin² x
= cos² x
= RHS
Hence verified.
Answer:
C ≈ 22.1°
Step-by-step explanation:
The law of cosines formula is given. Solving it for C, we find ...
C = arccos((a^2 +b^2 -c^2)/(2ab))
where a and b are the sides adjacent to the angle.
Then we have ...
C = arccos((14^2 +19^2 -8^2)/(2·14·19)) = arccos(493/532)
C ≈ 22.1°
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If you have a fair number of these to do, a spreadsheet is a useful tool. There are also triangle solver apps on the web or your local smart platform that will do this, too.
Step-by-step explanation:
option B is correct as,
10 + x = -18
→ x = -18 -10
→ x = -28
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