Question

If SinA =1/√2 then the value of CotA will be

Answer 1

Answer:

cotA=1

Step-by-step explanation:

sinA =p/B,1/✓2

cotA=B/P ,1/1=1

CotA =1

Answer 2

GIVEN :-

• given that sin a = 1 / √2

TO FIND :-

• value of cot a

SOLUTION :-

$\implies \rm{sin \: a = \dfrac{1}{ \sqrt{2} } }$

now squaring both sides ,

$\implies \rm{sin {}^{2} \: a = (\dfrac{1}{ \sqrt{2}}) {}^{2} }$

$\implies \rm{sin {}^{2} \: a = (\dfrac{1}{ {2}}) {}^{} }$

now we know that according to TRIGNOMETRIC IDENTITIES :-

$\implies \boxed {\rm{sin {}^{2} \: a + {cos}^{2} \: a = 1 }}$

hence ,

put the value of sin² a

$\implies \rm{ \: \dfrac{1}{2} + {cos}^{2} \: a = 1 }$

$\implies \rm{ \: {cos}^{2} \: a = 1 - \dfrac{1}{2} }$

$\implies \rm{ \: {cos}^{2} \: a = \dfrac{2 - 1}{2} }$

$\implies \rm{ \: {cos}^{2} \: a = \dfrac{ 1}{2} }$

$\implies \rm{ \: \sqrt{ {cos}^{2} \: a \: \: } = \sqrt{ \dfrac{ 1}{2} \: } }$

$\implies \rm{ \: cos\: a \: \: = \dfrac{ 1}{\sqrt{2 \: \: } \: }}$

$\implies \boxed{ \rm{ \: cot\: a \: \: = { \dfrac{ cos\: a}{s in \: a \: } \: }} }$

$\implies \boxed{ \boxed {\rm{ \: cot\: a \: \: = 1 }}}$

OTHER INFORMATION :-

TRIGNOMETRIC IDENTITIES

• sin²∅ + cos²∅ = 1

• sec²∅ - tan²∅ = 1

• cosec²∅ - cot²∅ = 1

TRIGNOMETRIC RATIOS

• sin ∅ = 1 / cosec ∅

• cos ∅ = 1 / sec ∅

• tan ∅ = 1 / cot ∅

TRIGNOMETRIC COMPLEMENTRY ANGLES

• sin ∅ = cos ( 90 - ∅ )

• cos ∅ = sin ( 90 - ∅ )

• sec ∅ = cosec ( 90 - ∅ )

• cosec ∅ = sec ( 90 - ∅ )

• tan ∅ = cot ( 90 - ∅ )

• cot ∅ = tan ( 90 - ∅ )