Express $\cot 75 ° + \cos 75 °$ in terms of trigonometric ratio of angles lying between $0 °$ and $45^{\circ} .$

Open in App

Solution

Finding the value of $\cot 75 ° + \cos 75 °$ :
Given $\cot 75 ° + \cos 75 °$
By using trigonometric identities:
$c o s (90 - θ) = s i n θ$
$\cot (90 - θ) = \tan θ$
So, the equation is
$= \cot (90 ° - 15) + \cos (90 ° - 15 °)$
$= \tan 15 ° + \sin 15 °$
Hence, the value of $\cot 75 ° + \cos 75 ° = \tan 15 ° + \sin 15 °$ .

Suggest Corrections

Similar questions

Q. Express the following in terms of trigonometric ratios of angles lying between 0 and 45:

cosec 54^{0} + sin 72^{0}

Q. Express the following in terms of trigonometric ratios of angles lying between 0 and 45:

sin 67^{0} + cos 75^{0}

Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

(i) sin67° + cos75°
(ii) cot65° + tan49°
(iii) sec78° + cosec56°
(iv) cosec54° + sin72°

Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

Q. Express the following in terms of trigonometric ratios of angles lying between

0^{\circ}

and

45^{\circ}

cot 85^{\circ} + cos 75^{\circ}

Join BYJU'S Learning Program

Express cot75°+cos75° in terms of trigonometric ratio of angles lying between 0° and 45∘.

Finding the value of cot75°+cos75°:Given cot75°+cos75°By using trigonometric identities:cos(90-θ)=sinθcot(90-θ)=tanθSo, the equation is =cot90°-15+cos90°-15°)=tan15°+sin15°Hence, the value of cot75°+cos75°=tan15°+sin15°.

Express $\cot 75 ° + \cos 75 °$ in terms of trigonometric ratio of angles lying between $0 °$ and $45^{\circ} .$