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Complementary angles: evaluate an expression in ratios of angles adding to 90 degrees

This type of question, asked 6 times: CDS 2 2016, CDS 1 2019, CDS 2 2019, CDS 2 2021, CDS 1 2022, CDS 1 2023. All 8 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    83
    Consider the following : 1. cos⁡75∘sin⁡15∘+sin⁡12∘cos⁡78∘−cos⁡18∘sin⁡72∘=1\frac{\cos 75^\circ}{\sin 15^\circ} + \frac{\sin 12^\circ}{\cos 78^\circ} - \frac{\cos 18^\circ}{\sin 72^\circ} = 1 2. cos⁡35∘sin⁡55∘−sin⁡11∘cos⁡79∘+cos⁡28∘cosec⁡62∘=1\frac{\cos 35^\circ}{\sin 55^\circ} - \frac{\sin 11^\circ}{\cos 79^\circ} + \cos 28^\circ \operatorname{cosec} 62^\circ = 1 3. sin⁡80∘cos⁡10∘−sin⁡59∘sec⁡31∘=0\frac{\sin 80^\circ}{\cos 10^\circ} - \sin 59^\circ \sec 31^\circ = 0 Which of the above are correct ?

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  2. Question 2

    CDS 2 2016

    75
    What is the value of cosec⁡268∘+sec⁡256∘−cot⁡234∘−tan⁡222∘\operatorname{cosec}^2 68^\circ + \sec^2 56^\circ - \cot^2 34^\circ - \tan^2 22^\circ ?

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  3. Question 3

    CDS 1 2019

    35
    What is the value of sin⁡19∘cos⁡71∘+cos⁡73∘sin⁡17∘\dfrac{\sin 19^\circ}{\cos 71^\circ} + \dfrac{\cos 73^\circ}{\sin 17^\circ} ?

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  4. Question 4

    CDS 2 2019

    52
    What is the value of sin⁡46∘cos⁡44∘+cos⁡46∘sin⁡44∘\sin 46^\circ \cos 44^\circ + \cos 46^\circ \sin 44^\circ ?

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  5. Question 5

    CDS 2 2021

    59
    If AA, BB and CC are interior angles of a triangle ABCABC, then what is tan⁡(B+C2)+sin⁡(B+C2)−cot⁡(A2)−cos⁡(A2)\tan\left(\frac{B+C}{2}\right) + \sin\left(\frac{B+C}{2}\right) - \cot\left(\frac{A}{2}\right) - \cos\left(\frac{A}{2}\right) equal to ?

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  6. Question 6

    CDS 2 2021

    54
    What is the value of sin⁡24∘sin⁡66∘−cos⁡24∘cos⁡66∘+tan⁡24∘tan⁡66∘−cot⁡24∘cot⁡66∘\sin 24^\circ\sin 66^\circ-\cos 24^\circ\cos 66^\circ+\tan 24^\circ\tan 66^\circ-\cot 24^\circ\cot 66^\circ ?

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  7. Question 7

    CDS 1 2022

    11
    What is the value of the following? 2sin⁡68∘cos⁡22∘−2cot⁡15∘5tan⁡75∘−3tan⁡20∘tan⁡40∘tan⁡45∘tan⁡50∘tan⁡70∘5\frac{2\sin 68^\circ}{\cos 22^\circ} - \frac{2\cot 15^\circ}{5\tan 75^\circ} - \frac{3\tan 20^\circ \tan 40^\circ \tan 45^\circ \tan 50^\circ \tan 70^\circ}{5}

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  8. Question 8

    CDS 1 2023

    51
    What is the value of cos⁡232∘+cos⁡258∘sec⁡250∘−cot⁡240∘+4tan⁡13∘tan⁡37∘tan⁡53∘tan⁡77∘\frac{\cos^2 32^\circ + \cos^2 58^\circ}{\sec^2 50^\circ - \cot^2 40^\circ} + 4\tan 13^\circ \tan 37^\circ \tan 53^\circ \tan 77^\circ ?

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