Question

using trigonometrical identities... correct answer will be marked as brainliest and his or her account will be followed ​

Answer 1

Answer:

(sin(90-55) cos55 +cos(90-55) sin55)/cosec^2 (90- 80) -tan^2 80

(cos^2 55 + sin^2 55) / (sec^2 80 - tan^2 80)

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1 answer

Answer 2

$\huge \mathfrak \pink{answer}$

$\bf{ \huge{ \boxed{ \red{ \tt{1 \: }}}}}$

❖___________________________❖

❖step to step explanation ❖

$\rm{ \frac{sin35cos35 + cos35sin35}{ {cosec}^{2}10 - {tan}^{2} 80} }$

$\rm{ \frac{sin(35 + 55}{ {cosec}^{2}10 - {tan}^{2}(90 - 10}}$

$\rm{ \frac{sin90}{ {cosec}^{2}10 - {cot}^{2}10} }$

$\rm{ \frac{1}{1}}$

$\rm \green{ = 1}$

(or)

❁step to step explanation ❁

$\sf{ \sin35= sin(90 - 55) = cos55}$

$\sf{cos35 = sin(90 - 55) = sin55}$

$\sf{tan80 = tan(90 - 10) = cot10}$

__________________________

$\rm \red{ {sin}^{2}a + {cos}^{2}a = 1}$

$\rm \red{ {cosec}^{2}a + {cot}^{2}a = 1}$

then

$\tt \blue{ \frac{ {cos}^{2}55 + {sin}^{2}55}{ {cosec}^{2}10 - {cot}^{2}10 } = \frac{1}{1} = 1}$

Answer is 1