PYQ Vault
EbooksTutor

Evaluate an expression of complementary angles (sin x = cos(90 - x), sec^2 - tan^2 = 1 across pairs)

This type of question, asked 6 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II, 2 Mar 2023 Tier II, 18 Jan 2026 Tier II. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    15 Nov 2020 Tier II

    39
    The value of 2sin⁡238∘sec⁡252∘+cos⁡64∘sin⁡26∘+sin⁡264∘tan⁡223∘+cot⁡223∘−sec⁡267∘−cosec267∘\frac{2\sin^2 38^\circ \sec^2 52^\circ + \cos 64^\circ \sin 26^\circ + \sin^2 64^\circ}{\tan^2 23^\circ + \cot^2 23^\circ - \sec^2 67^\circ - \text{cosec}^2 67^\circ} is:

    Tap an option to check your answer.

  2. Question 2

    29 Jan 2022 Tier II

    9
    The value of 3(cot⁡247∘−sec⁡243∘)−2(tan⁡223∘−cosec267∘)cosec2(68∘+θ)−tan⁡(θ+61∘)−tan⁡2(22∘−θ)+cot⁡(29∘−θ)\frac{3(\cot^2 47^\circ - \sec^2 43^\circ) - 2(\tan^2 23^\circ - \text{cosec}^2 67^\circ)}{\text{cosec}^2(68^\circ + \theta) - \tan(\theta + 61^\circ) - \tan^2(22^\circ - \theta) + \cot(29^\circ - \theta)} is:

    Tap an option to check your answer.

  3. Question 3

    29 Jan 2022 Tier II

    94
    The value of 4tan⁡230∘+sin⁡230∘cos⁡245∘+sec⁡248∘−cot⁡242∘cos⁡37∘sin⁡53∘+sin⁡37∘cos⁡53∘+tan⁡18∘tan⁡72∘\frac{4\tan^2 30^\circ + \sin^2 30^\circ\cos^2 45^\circ + \sec^2 48^\circ - \cot^2 42^\circ}{\cos 37^\circ\sin 53^\circ + \sin 37^\circ\cos 53^\circ + \tan 18^\circ\tan 72^\circ} is:

    Tap an option to check your answer.

  4. Question 4

    3 Feb 2022 Tier II

    13
    The value of 3(cosec226∘−tan⁡264∘)+(cot⁡242∘−sec⁡248∘)cot⁡(22∘−θ)−cosec2(62∘+θ)−tan⁡(θ+68∘)+tan⁡2(28∘−θ)\frac{3(\text{cosec}^2 26^\circ - \tan^2 64^\circ) + (\cot^2 42^\circ - \sec^2 48^\circ)}{\cot(22^\circ - \theta) - \text{cosec}^2(62^\circ + \theta) - \tan(\theta + 68^\circ) + \tan^2(28^\circ - \theta)} is:

    Tap an option to check your answer.

  5. Question 5

    3 Feb 2022 Tier II

    67
    The value of (cos⁡9∘+sin⁡81∘)(sec⁡9∘+cosec⁡81∘)cosec⁡271∘+cos⁡215∘−tan⁡219∘+cos⁡275∘\frac{(\cos 9^\circ + \sin 81^\circ)(\sec 9^\circ + \operatorname{cosec} 81^\circ)}{\operatorname{cosec}^2 71^\circ + \cos^2 15^\circ - \tan^2 19^\circ + \cos^2 75^\circ} is:

    Tap an option to check your answer.

  6. Question 6

    8 Aug 2022 Tier II

    43
    What is the value of cos⁡50∘sin⁡40∘+3 cosec 80∘sec⁡10∘−2cos⁡50∘.cosec 40∘\frac{\cos 50^\circ}{\sin 40^\circ} + \frac{3\,\text{cosec}\,80^\circ}{\sec 10^\circ} - 2\cos 50^\circ . \text{cosec}\,40^\circ ?

    Tap an option to check your answer.

  7. Question 7

    8 Aug 2022 Tier II

    76
    What is the value of 3sin⁡58∘cos⁡32∘+3sin⁡42∘cos⁡48∘\frac{3\sin 58^\circ}{\cos 32^\circ} + \frac{3\sin 42^\circ}{\cos 48^\circ}?

    Tap an option to check your answer.

  8. Question 8

    2 Mar 2023 Tier II

    18
    Evaluate the following. sin⁡25∘sin⁡65∘−cos⁡25∘cos⁡65∘\sin 25^\circ \sin 65^\circ - \cos 25^\circ \cos 65^\circ.

    Tap an option to check your answer.

  9. Question 9

    18 Jan 2026 Tier II

    5
    What is the value of 32(cos⁡39sin⁡51)−sin⁡239∘+sin⁡251∘\frac{3}{2}\left(\frac{\cos 39}{\sin 51}\right) - \sqrt{\sin^2 39^\circ + \sin^2 51^\circ} ?

    Tap an option to check your answer.