(sin+sec)²+ (cose + cosec)²= (1+sece coseco)²
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Answered by
2
Step-by-step explanation:
LHS=(sinA+secA)
2
+(cosA+cosecA)
2
=sin
2
A+2sinAsecA+sec
2
A+cos
2
A+2cosAcosecA+cosec
2
A
=(sin
2
A+cos
2
A)+(sec
2
A+cosec
2
A)+2sinAsecA+2cosAcosecA
=1+(
cos
2
A
1
+
sin
2
A
1
)+2
cosA
sinA
+2
sinA
cosA
(∵sin
2
A+cos
2
A=1)
=1+(
cos
2
Asin
2
A
sin
2
A+cos
2
A
)+2(
cosAsinA
sin
2
A+cos
2
A
)
=1+(
cos
2
Asin
2
A
1
)+2(
cosAsinA
1
)
=1+sec
2
Acosec
2
A+2secAcosecA
=(1+secAcosecA)
2
=RHS
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