prove that
[tex] \frac{ \sin \: a \tan \: a }{1 - \cos \: a} = 1 + \sec \: a [/tex]
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prove that
[tex] \frac{ \sin \: a \tan \: a }{1 - \cos \: a} = 1 + \sec \: a [/tex]
no spam ❌❌❌
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Answer:
[tex] \frac{ \sin \: a \: \tan \: a }{1 - \cos \: a } = \frac{ { \sin \: a }^{2} }{ \cos \: a \: (1 - \cos \: a) } \\ = \frac{1 - { \cos}^{2} \: a}{ \cos \: a \: ( 1 - \cos \: a) } \\ = \frac{1 + \cos \: a }{ \cos \: a } \\ = \frac{ \sin \: a \: \tan \: a }{1 - \cos \: a} = 1 + \sec \: a[/tex]
hence proved
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Answer:
In this type of question first you have to change tan \a\a
in \bold{ \frac{sina}{cosa} }
cosa
sina
form then you have to use the suitable identity.
\bold{ tan \: a \: = \frac{sin \: a}{cos \: a} }tana=
cosa
sina
Identity used :-
\bold{{ \sin}^{2} a = 1 - {cos}^{2} a }sin
2
a=1−cos
2
a
Dear!! User kindly refer to attachment.
Step-by-step explanation:
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