Prove: 1/ 1 + cos A + 1/ 1 – cos A = 2 cosec^2A
Prove:
\[\begin{array}{*{35}{l}} RHS\text{ }=\text{ }ta{{n}^{2}}~A\text{ }+\text{ }co{{t}^{2}}~A\text{ }+\text{ }2\text{ }=\text{ }ta{{n}^{2}}~A\text{ }+\text{ }co{{t}^{2}}~A\text{ }+\text{ }2\text{...
Prove:
\[\begin{array}{*{35}{l}} LHS, \\ {{\left( sin\text{ }A\text{ }+\text{ }cosec\text{ }A \right)}^{2}}~+\text{ }{{\left( cos\text{ }A\text{ }+\text{ }sec\text{ }A \right)}^{2}} \\ =\text{...
Prove: sec A – tan A/ sec A + tan A = 1 – 2 secA tanA + 2 tan^2 A
= 1 + tan2 A + tan2 A – 2 sec A tan A = 1 – 2 sec A tan A + 2 tan2 A = RHS
Prove: cosec A + cot A = 1/ cosec A – cot A
cosec A + cot A
Prove: 1/ sec A + tan A = sec A – tan A
Prove: (cosec A – sin A)(sec A – cos A)(tan A + cot A) = 1
(cosec A – sin A)(sec A – cos A)(tan A + cot A)
Prove:
\[\begin{array}{*{35}{l}} {{\left( cos\text{ }A\text{ }+\text{ }sin\text{ }A \right)}^{2}}~+\text{ }{{\left( cosA\text{ }-\text{ }sin\text{ }A \right)}^{2}} \\ =\text{ }cos2\text{ }A\text{ }+\text{...
Prove:
\[\begin{array}{*{35}{l}} \left( sec\text{ }A\text{ }-\text{ }cos\text{ }A \right)\left( sec\text{ }A\text{ }+\text{ }cos\text{ }A \right) \\ =\text{ }\left( se{{c}^{2}}~A\text{ }-\text{...
Prove:
\[\begin{array}{*{35}{l}} \left( cosec\text{ }A\text{ }+\text{ }sin\text{ }A \right)\text{ }\left( cosec\text{ }A\text{ }-\text{ }sin\text{ }A \right) \\ =\text{ }cose{{c}^{2}}~A\text{ }-\text{...
Prove:
cot2 A – cos2 A
Prove:
tan2 A – sin2 A
Prove:
Prove
Prove: cosec A (1 + cos A) (cosec A – cot A) = 1
Prove: sec A (1 – sin A) (sec A + tan A) = 1
sec A (1 – sin A) (sec A + tan A)
Prove: cosec^4 A – cosec^2 A = cot^4 A + cot^2 A
\[\begin{array}{*{35}{l}} cose{{c}^{4}}~A\text{ }-\text{ }cose{{c}^{2}}~A \\ =\text{ }cose{{c}^{2}}~A\left( cose{{c}^{2}}~A\text{ }-\text{ }1 \right) \\ =\text{ }\left( 1\text{ }+\text{...
Prove: (1 – tan A)^2 + (1 + tan A)^2 = 2sec^2 A
\[\begin{array}{*{35}{l}} {} \\ {{\left( 1\text{ }-\text{ }tan\text{ }A \right)}^{2}}~+\text{ }{{\left( 1\text{ }+\text{ }tan\text{ }A \right)}^{2}} \\ =\text{ }\left( 1\text{ }+\text{...
Prove the following : sin^4 A – cos^4 A = 2 sin^2 A – 1
\[\begin{array}{*{35}{l}} \mathbf{L}.\mathbf{H}.\mathbf{S}, \\ si{{n}^{4}}~A\text{ }-\text{ }co{{s}^{4}}~A \\ =\text{ }{{\left( si{{n}^{2~}}A \right)}^{2}}~-\text{ }{{\left( co{{s}^{2}}~A...