tan
-
Sino
+ Coso
. 2 coto
seco-1
Answers
Answer:
sin cos theta equals to sin theta
Answer:
LHS:
\begin{lgathered}(\frac{tan \: a}{sec \: a - 1} ) - ( \frac{sin \: a}{1 + cos \: a} ) = 2 \: cot \: a \\ ( \frac{ \frac{sin \: a}{cos \: a} }{ \frac{1 - cos \: a}{cos \: a} } ) - ( \frac{sin \: a}{1 + cos \: a} ) \\ ( \frac{sin \: a}{1 - cos \: a} ) - ( \frac{sin \: a}{1 + cos \: a} ) \\ ( \frac{sin \: a(1 + cos \: a) - sin \: a(1 - cos \: a)}{(1 - cos \: a)(1 + cos \: a)} \\ \frac{sin \: a + sin \: a \: cos \: a - sin \: a + sin \: a \: cos \: a}{ {sin}^{2}a } \\ \frac{2sin \: a \: cos \: a}{ {sin}^{2} a} \\ \\ 2 \frac{cos \: a}{sin \: a} \\ \\ 2cot \: a\end{lgathered}
(
seca−1
tana
)−(
1+cosa
sina
)=2cota
(
cosa
1−cosa
cosa
sina
)−(
1+cosa
sina
)
(
1−cosa
sina
)−(
1+cosa
sina
)
(
(1−cosa)(1+cosa)
sina(1+cosa)−sina(1−cosa)
sin
2
a
sina+sinacosa−sina+sinacosa
sin
2
a
2sinacosa
2
sina
cosa
2cota
LHS = RHS
Hence proved
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