Question

please help me in matching​

Answer 1

Answer::

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$\large\blue{\rm\:Answer}$

TRIGONOMETRY:

$\bf\blue{Matrix\: matching:}}</p><p></p><h2>coloumn-(I) </h2><p>[tex]\bf\red{(3) If\: sin\theta=cos\theta \: ,then \: theta=?}$

$\sf\pink{As \: know \: that \:}$

$\sf\pink{sin\theta=sin(\dfrac{pi}{2}-\theta)=cos\theta }$

$\sf{sin\theta=cos\theta [Answer]=90degree }$

$\bf\brown{option\: (d) \:90 degree\: is\: correct }$

$\bf\red{(4)\: cos(A+B)=\dfrac{1}{2}\: and \: sin(A-B) =\dfrac{1}{2}}$

$\implies\sf{As \: we\: know\:that cos(\dfrac{1}{2}=60degree\: and \: sin(\dfrac{1}{2}=30degree}$

$\sf{A+B=60 \: and \:A-B=30degree}$

$\sf{A+B=60}$......(1)

$\sf{A-B=30}$.......(2)

$\bf{2A=90}$

$\bf{A=45}$

now put the A value in eqn (1)

$\bf{45+B=60}$

$\bf{B=15degree}$

$\bf\green{option\:(a) \: is\: corrrect}$

$\bf\red{(5)tan\theta=90 degree =not defined }$

$\bf\green{option(d) \: is\: correct}$

$\bf\red{(6) tan^2\theta=\dfrac{1+cos60}{1-cos60}$

$\implies\sf{tan^2\theta=\dfrac{1+\dfrac{1}{2}{1-\dfrac{1/2}}$

$\implies\sf{tan^2\theta=1}$

$\implies\sf{\theta=45degree}$